Vol. 55, No. 1

V.L. Makarovi,*, A.R. Bakhtizini, G.L. Beklaryani, A.S. Akopovi, E.A. Rovenskayaii,**, N.V. Strelkovskiyii Aggregated agent-based simulation model of migration flows of the European Union countries
Economics and mathematical methods
, 2019, 55 (1), 3-15.

      i Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia
      ii International Institute for Applied Systems Analysis, Laxenburg, Austria
      * E-mail:
      ** E-mail:
This study was financial partially supported by the Russian Foundation for Basic Research (project 18-51-14010 _).

Abstract. This article presents the aggregated agent-based simulation model of migration flows of the European Union (EU) countries, implemented in the AnyLogic system, created in the form of an extended "gravity model", according to which individual decisions by agent-migrants are based on the integrated assessment of socio-economic, geographical and other differentiation of the respective countries. At the same time, some factors 'attract' migrants, while others 'repel'. A distinctive feature of the model is the differentiation of migration flows by the categories of migrants with the release of various influencing factors that reflect the individual preferences of agent-migrants regarding to the agents-countries (EU members). At the same time, there are multiple control parameters that affect the distribution of migration flows between the EU countries, in particular, migration quotas, unemployment benefits, minimum wages, etc. The most important bicriterial optimization task of EU countries for choosing rational migration and economic policies based on maximizing integral GDP and minimizing the total number of migrants has been formulated. The issue is aimed to control parameters that affect the structure of migration flows and labor resources, as well as their maintenance costs. For the first time, an expanded gravitational model has been proposed and studied, describing dynamic migration flows with the release of multiple factors that differentiate the attractiveness of EU countries for various groups of migrants, for example, internal migrants, economic migrants, refugees, etc.
Keywords: agent-based modeling of migration flows, multi-criteria optimization, AnyLogic, problems of migration to the EU.
JEL Classification: B23, F22, J61.
DOI: 10.31857/S042473880004044-7

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Beklaryan G.L. (2018). Aggregated Simulation Model of Foreign Economic Activity of the Russian Federation. Economic Science of Contemporary Russia, 4, 50-65 (in Russian).
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V.E. Dementievi,*, E.V. Ustyuzhaninaii,** Comparative Analysis of Dynamic Pricing Strategies in Markets of Network Goods (Cases of Monopoly and Precompetitive Strategic Alliances)
Economics and mathematical methods
, 2019, 55 (1), 16-31.

      i Central Economics and Mathematics Institute RAS , Moscow, Russia
      ii Plekhanov Russian University of Economics , Moscow, Russia
      * E-mail:
      ** E-mail:
This study was financially supported by the Russian Foundation for Basic Research (project 17-06-00080) "Comparative analysis of pricing strategies in markets of network goods on the basis of economic and mathematical modeling".

Abstract. The paper describes pricing strategies in markets of network goods. Such markets are characterized by the need to achieve critical mass. The authors analyze how the dynamic pricing with the aim of increasing the number of consumers can affect the net present income of a monopoly supplier. Two options of dynamic pricing are considered. In the first case prices represent a share of a good's utility for a consumer, the value of which depends on the already existing number of consumers. The second option consists of two stages. In the first stage consumers get a network good for free - the aim is to increase the number of consumers as fast as possible. In the second stage prices represent a share of a good's utility - like in the first case. Examples of pricing strategies that maximize the net present income in both cases are given. It is particularly difficult to achieve critical mass when investment costs are high. One possible solution would be to create strategic alliances. The authors describe a situation when after precompetitive cooperation the firms choose different pricing strategies. One of the firms tries to outrun its competitors in terms of market share by choosing a low-price strategy. Another one seeks to take advantage of the "market warming up" provided by a competitor. The intensity of consumers' reaction to differences in suppliers' prices can be regarded as one of the key features of the market. The authors analyze how changes in this feature can affect the outcomes of competitors with different pricing strategies.
Keywords: network goods, dynamic pricing, strategic alliances, monopoly, duopoly.
JEL Classification: D46, G30, C12.
DOI: 10.31857/S042473880003986-3

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Cabral L.M.B., Salant D.J., Woroch G.A. (1999). Monopoly Pricing with Network Externalities. International Journal of Industrial Organization, 17, 2, 199-214.
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Dementiev V.E., Evsyukov S. G., Ustyuzhanina E.V. (2018). Pricing Model in the Market for Network Goods in Terms of Duopolistic Competition. Economics and Mathematical Methods, 54, 1, 26-42 (in Russian).
Economides N. (1996). The Economics of Networks. International Journal of Industrial Organization, 14, 2, 673-699.
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Kozyrev A.N. Optimizing the placement of interconnected R&D based on double auction
Economics and mathematical methods
, 2019, 55 (1), 32-42.

      Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia
Received 23.05.2018

Abstract. The article is based on the results of the research on the program "National economic security of Russia in conditions of aggravation of objective and initiated risks and threats" 2017 of the Social Sciences Department of the Russian Academy of Sciences. The aim of this paper is to suggest effective solution based on the theory of smart markets for distribution of R & D among potential executors (actors). Suggested solution is the original modification of the smart market model obtained as a 2-replica of the well-known intra-firm knowledge market model. It is shown that the 2-replica retains the main advantages of the original model including compatibility with incentives. The model allows combining computational efficiency and competition elements for some impotent special case. If there is only one performer for each job the optimal solution is calculated quite easily. The same easily the optimal solution is obtained for 2-replica. There is no monopoly in 2-replica, but there is another problem. Optimal solution is determined not uniquely. To get rid of ambiguity it is proposed to modify the model by introducing random deviations when evaluating their packages by agents and compensation to agents is determined by the rule of the second price. It is proved that the resulting scheme of choice of actors is compatible with incentives. Some economic interpretation of the results is given.
Keywords: knowledge, compatibility with incentives, smart market, double auction.
JEL Classification: C79, O32.
DOI: 10.31857/S042473880004026-7

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E.G. Vinokurovi, ii, V.P. Meshalkini, Kh.A. Nevmyatullinai, ii,*, T.F. Burukhinai, V.V.Bondarii, S.M. Khodchenkoi Method of the Modified SWOT-Analysis of the Effectiveness of Technology Changes
Economics and mathematical methods
, 2019, 55 (1), 43-55.

      i Dmitry Mendeleev University of Chemical Technology of Russia, Moscow, Russia
      ii Russian Institute for Scientific and Technical Information (VINITI RAS) , Moscow, Russia
      * E-mail:
This investigation was supported Ministry of Science and Education of Russian Federation, 10.4556.2017/6.7

Abstract. Currently, the classical SWOT-analysis is widely used for assessing competitiveness and design a strategy for the development of the management object. The method provides only qualitative assessment of technical and economic efficiency. At the same time only one object (technology, industry, organization, division of the enterprise and other similar objects) is analyzed the effectiveness. The authors propose a new modified nonparametric-statistical method of SWOT-analysis to compare the effectiveness of two control objects. The stages of analysis are described: the choosing of a group of experts, the development of a questionnaire for their survey, the survey, the formation of a modified matrix of SWOT-analysis. The samples of modified SWOT-analysis matrices were developed both separately for each object and for the compared objects in the aggregate. To ensure the reliability of the results, the modified SWOT-analysis method is added with the criterion of nonparametric statistics, which is used to quantify the reliability of shifts - the criterion of signs (G-criterion). An algorithm for applying the criterion to test the hypothesis of the direction of the shift in the performance indicators in the change one object to another is presented. The proposed method was applied for the comparison of technical and economic efficiency of the two processes of chromium plating from solutions based on toxic chromic acid (Cr-6) and from baths based on less environmentally hazardous substances of trivalent chromium (Cr-3). It is shown that now the technology (Cr-6) is more effective technology for the production of chrome coatings then (Cr-3) technology. Perhaps more effective is to carry out modernization of the classical technology (Cr-6).
Keywords: SWOT-analysis, non-parametric statistics, sign criterion, technical economical efficiency, technologies, chemical engineering, electrodeposition, plating, chromium.
JEL Classification: C19, L60, M11, O32.
DOI: 10.31857/S042473880004046-9

      REFERENCES (with English translation or transliteration)
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Azarko O.E., Kuznetsov V.V., Shakhamayer S.R., Vinokurov E.G. (1997). Electrodeposition of Thick Hard Chromium Coatings from Bath on the Based of Trivalent Chromium. Electroplating & Surface Treatment, 5, 4, 25-32 (in Russian).
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Fadina S.V., Vinokurov E.G., Burukhina T.F., Kolesnikov V.A. (2013). Total Concentration of Main Components in Solutions for Metal Electroplating as a Criterion for Classifying and Choosing Resource-Saving Compositions of Solutions. Theoretical Foundations of Chemical Engineering, 47, 5, 593-599.
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Jiang Y., Xie W., Zhuang B. (2017). The Civil-Military Integration Development of Equipment Construction Based on SWOT Quantitative Method. In: "Proceedings of the 29th Chinese Control and Decision Conference". CCDC 2017/ 7979280, 4439-4443.
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Vinokurov E.G., Meshalkin V.P., Vasilenko E.A., Nevmytullina Kh.A., Burukhina T.F., Bondar V.V. (2016). System Analysis of the Efficiency and Competitiveness of Chroming Technologies. Theoretical Foundations of Chemical Engineering, 50, 5, 730-738.
Vinokurov E.G., Burukhina T.F., Kolesnikov V.A., Fadina S.V. (2012). Concentration Criterion for Classifying Resource-Saving Compositions of Solutions for Metal Electroplating. Theoretical Foundations of Chemical Engineering, 46, 5, 486-491.
Vinokurov E.G., Nevmyatullina Kh.A., Burukhina T.F. Grafushin R.V., Bondar V.V. (2016). SWOT-Analysis of hromium Plating. Kompetentnost', 4, 27-32 (in Rissian).
Yurlov F.F., Plekhanova A.F., Bobkova T.V. Kolesov K.I., Bolonicheva T.V., Galkin K.B. (2013). Strategic Planning of Scientific-Production Associations and Industrial Enterprises on the Basis of Portfolio and SWOT Analysis. Nizhniy Novgorod: Nizhegorodskiy gosudarstvenniy universiyey im. R.E. Alekseeva (in Russian).

L.E. Mindeli*, S.F. Ostapyuk**, V.P. Fetisov*** On long-term prediction of fundamental and exploratory research
Economics and mathematical methods
, 2019, 55 (1), 56-67.

      Institute of development of science of Russian Academy of Sciences, Moscow, Russia
      * E-mail: L. Mindeli
      ** E-mail: S.
      *** E-mail: V. Fetisov@

Abstract. A basic precondition for the solution of the ambitious task - Russia entering the club of five largest economies in the worlds, set by the President of the Russian Federation, - is consolidation and joint actions of the participants in the strategic planning, ensuring the development of socio-economic and scientific-technological spheres of activity. The original threshold document determining the prospects for their development is the prediction of socio-economic and scientific-technological development, forecast of the progress in science, including the basic research. Prediction of fundamental and exploratory research (pilot-study) is the responsibility of the Russian Academy of Sciences. However, as evidenced by the analysis, forecasting procedure of these activities, in contrast to the socio-economic and scientific-technological development, is not legally regulated. Ways to eliminate this gap is the subject of the study. The work outlines the subject and steps in the procedure of long-term forecasting in the scientific and technical spheres. The analysis of normative and legal basis of the formation of aggregated long-term forecast models for fundamental and exploratory research defined terms and stages of such rules' development for aggregate models, formulated the methodological features and requirements of these regulations, as well as the proposals for the development of its expertise tools and information support. The study laid the basis for preparing and taking the government decision on regulation of predicting fundamental and exploratory research providing RAS with the responsible status on predicting fundamental and pilot-studies. It is emphasized that the procedure and the development model specified matches the national forecasting model, certain decisions of the Government of the Russian Federation on the procedure of forecasting the socio-economic, scientific and technological development. At the same time, the model considers the differences in forecasting problems of development of fundamental and applied scientific types of research.
Keywords: fundamental and pilot-study, socio-economic and scientific-technological development, procedure and model of long-term forecasting, strategic planning, legislation, methodological and information provision, institute and rules of regulations.
JEL Classification: E17, B4, I23.
DOI: 10.31857/S042473880004047-0

      REFERENCES (with English translation or transliteration)
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D.O. Afanasyev1,*, E.A. Fedorova2,** Short-term electricity price forecasting on the Russian market using the SCARX models class
Economics and mathematical methods
, 2019, 55 (1), 68-84.

      1 Postgraduate student of the Data Analysis, Decision Making and Financial Technologies Department; Financial University under the Government of the Russian Federation, Moscow, Russia
      2 Financial Management Department Financial University under the Government of the Russian Federation; Finance Department - Higher School of Economics, Moscow, Russia
      * E-mail:
      ** E-mail:
The presented study was funded by the Russian Foundation for Basic Research (RFBR) within research project No. 16-06-00237 A.

Abstract. This research is focused on the approbation of Seasonal Component AutoRegressive with exogenous factors (SCARX) forecasting models class on two price area of the Russian electricity market. The SCARX model consists of extrapolation of long-term trend-seasonal component and independent forecasting of short-term seasonal-stochastic component of electricity price. The SCARX based on wavelet decomposition (SCARX-W) and Hodrick-Prescott filter (SCARX-HP) for the wide range of time-series smoothing parameters are compared with the usual autoregression model ARX and na?ve approach (based on assumption of the price similarity in the same weekday). The performance evaluation was carried out using weighted weekly and daily mean absolute errors, as well as the formal statistical procedure of the prediction ability comparison - Diebold-Mariano test (DM-test). The historical data of price and planed consumption in the Europe-Ural and Siberia price areas of the Russian electricity exchange were used for the numerical experiment, while testing period is 104 week or 728 days long. The study shows that in the Russian markets SCARX-W model exhibits more accurate forecast compare to SCARX-HP and ARX. The minimal weekly error achieved on Europe-Ural price area is 4,932%, daily error - 4,997%. The same indicators for Siberia price area are 9,144% and 10,051%, correspondingly. The same results are proved by the formal DM-test carried for each hour in trading day. In order to overcome the problem of a priori selection of smoothing parameters, it is proposed to use various methods of forecast combinations.
Keywords: electricity price forecasting, seasonal component autoregressive, wavelet-smoothng, Hodrick-Prescott filter, Diebold-Mariano test.
JEL Classification: C22, C53, L94, Q47.
DOI: 10.31857/S042473880003318-8

      REFERENCES (with English translation or transliteration)
Afanasyev D., Fedorova E. (2016). The Long-Term Trends on the Electricity Markets: Comparison of Empirical Mode and Wavelet Decompositions. Energy Economics, 56, 432-442.
Carmon R., Coulon M. (2014). A Survey of Commodity Markets and Structural Models for Electricity Prices. In: "Modeling, Pricing, and Hedging in Energy and Commodity Markets". New York: Springer.
Casazza J., Delea F. (2003). Understanding Electric Power Systems: An Overview of the Technology and the Marketplace. Hoboken: Wiley.
Chuchueva I.A. (2012). The Time Series Forecasting Model with Maximum Likeness Sample. Postgraduate thesis. Moscow: BMSTU.
Conejo A.J., Contreras J., Espinola R., Plazas M.A. (2005). Forecasting Electricity Prices for a Day-Ahead Pool-Based Electric Energy Market. International Journal of Forecasting, 21, 3, 435-462.
De Jong C. (2006). The Nature of Power Spikes: A Regime-Switch Approach. Studies in Nonlinear Dynamics and Econometrics, 10, 3, 35-47.
Diebold F.X., Mariano R.S. (1995). Comparing Predictive Accuracy. Journal of Business and Economic Statistics, 13, 253-263.
Eydeland A., Wolyniec K. (2012). Energy and Power Risk Management. New Jersey: Wiley.
Fedorova E., Afanasyev D. (2015). Study of the Dynamic Price-Demand Relationship for Russian Electricity Market. Proceedings of the Russian Academy of Sciences. Power Engineering, 3, 3-17 (in Russian).
Haldrup N., Nielsen F., Nielsen M. (2010). A Vector Autoregressive Model for Electricity Prices Subject to Long Memory and Regime Switching. Energy Economics, 32, 1044-1058.
Hodrick R., Prescott E. (1997). Postwar U.S. Business Cycles: An Empirical Investigation. Journal of Money, Credit and Banking, 29, 1, 1-16.
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Janczura J., Tr?ck S., Weron R., Wolff R. (2013). Identifying Spikes and Seasonal Components in Electricity Spot Price Data: A Guide to Robust Modeling. Energy Economics, 38, 96-110.
Lisi F., Nan F. (2014). Component Estimation for Electricity Prices: Procedures and Comparisons, Energy Economics, 44, 143-159.
Maciejowska K., Nowotarski J., Weron R. (2016). Probabilistic Forecasting of Electricity Spot Prices Using Factor Quantile Regression Averaging. International Journal of Forecasting, 32, 3, 957-965.
Maciejowska K., Weron R. (2016). Short- and Mid-Term Forecasting of Baseload Electricity Prices in the UK: The Impact of Intra-Day Price Relationships and Market Fundamentals. IEEE Transactions on Power Systems, 31, 2, 994-1005.
Misiorek A., Tr?ck S., Weron R. (2006). Point and Interval Forecasting of Spot Electricity Prices: Linear vs. Non-Linear Time Series Models. Studies in Nonlinear Dynamics and Econometrics, 10, 3, 57-66.
Nogales F.J., Contreras J., Conejo A.J., Espinola R. (2002). Forecasting Next-Day Electricity Prices by Time Series Models. IEEE Transactions on Power Systems, 17, 342-348.
Nowotarski J., Raviv E., Tr?ck S., Weron R. (2014). An Empirical Comparison of Alternative Schemes for Combining Electricity Spot Price Forecasts. Energy Economics, 46, 342-348.
Nowotarski J., Tomczyk J., Weron R. (2013). Robust Estimation and Forecasting of the Long-Term Seasonal Component of Electricity Spot Prices. Energy Economics, 39, 13-27.
Nowotarski J., Weron R. (2016). On the Importance of the Long-Term Seasonal Component in Day-Ahead Electricity Price Forecasting. Energy Economics, 57, 228-235.
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Weron R. (2014). Electricity Price Forecasting: A Review of the State-of-the-Art with a Look into the Future. International Journal of Forecasting, 30, 1030-1081.
Weron R., Zator M. (2015). A Note on Using the Hodrick-Prescott Filter in Electricity Markets. Energy Economics, 48, 1-6.

Danilin V.I.* System Models Horizontal Harmonization of Planning Decisions by Various units of the Company
Economics and mathematical methods
, 2019, 55 (1), 85-100.

      Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia
      * E-mail:

Abstract. In developing a business plan, take part in almost all company departments, such as purchasing department, production department or the planning and Economic Department, Finance Department, Sales Department and others. Each unit develops its own section of the plan, on the basis of their specific objectives, which did not always coincide with the objectives of the company as a whole. This raises the problem of harmonizing these decisions with the company's goals. There are different approaches to solving the problem of harmonization. For example, vertical alignment, when units are in detail its decisions in aggregated form and pass them in the direction where on that basis accepted the final version of the plan of the company and the results are on the level of units for rework. This article focuses on the development of a system of models horizontal harmonization of planning decisions between units. To solve this problem, the methodology of the sequence of decision-making entities in the form of an iterative procedure based on system models. The system consists of a model production plan in view of the expansion of capacities, model financial plan (plan for profits and losses, planned balance and cash flow plan), the company's marketing plan model and model supply plan given the inverse relationships between models. The example shows that after a number of iterations units receive a consistent routine decision corresponding to the objectives of the company as a whole.
Keywords: functional units, production and financial divisions, the first division of supply and sales, negotiate solutions, system models, stages (iteration) the formulation of the plan.
JEL Classification: D2, D24, L2, G32.
DOI: 10.31857/S042473880003985-2

      REFERENCES (with English translation or transliteration)
Ashimov A.A., Burkov V.N., Dzhaparov B.A., Kondrat'ev V.V. (1986). Consistent Management of Active Production Systems. Moscow: Nauka (in Russian).
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Danilin V. (2006). Operational and Financial Planning in Corporations (Methods and Models). Moscow: Nauka (in Russian).
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Yu.N. Gavrilets*, M. V. Chernenkov**, S.A. Nikitin*** Aggregated Indices of Public Opinion on the Life Quality in Russian Regions
Economics and mathematical methods
, 2019, 55 (1), 101-115.

      Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia
      * E-mail:
      ** E-mail:
      *** E-mail:
This study was supported by the Russian Science Foundation (project 17-18-01080).

Abstract. The article offers methodological approaches to the study of features and differences in the population's assessments of living conditions in the regions of Russia. An attempt is made to build aggregated indices that characterize the economic growth potential, the aggregate opinion and estimates of the population of regions, the social concern of citizens and the level of public security. For this purpose, we use data from special sociological surveys and official statistics on 47 subjects of the Russian Federation. Aggregated indices are calculated using the principal component method. Statistical relationships between the constructed indices are investigated, a regression model is constructed that characterizes the dependence of the population's satisfaction on living conditions from the level of economic potential, concern and trust to law enforcement agencies. A comparative analysis of the possibilities of economic growth of regions, levels of satisfaction and concern of the population is carried out. The dynamics of economic potential growth in the regions of the Russian Federation is also analyzed, taking into account the possibility of forecasting and application in social management.
Keywords: regions of Russia, sociological research, quality of life, social concern, economic potential, regional security, main components method, regression analysis, conditional forecast.
JEL Classification: C53.
DOI: 10.31857/S042473880004045-8

      REFERENCES (with English translation or transliteration)
Aivasyan S. (2012). Analysis of the Quality and Lifestyle of the Population. Econometric Approach. Moscow: Nauka (in Russian).
Aivasyan S., Afanasiev M., Kudrov A. (2016). Clustering Method of Regions of the Russian Federation Taking into Account the Sectoral Structure of GRP. Applied Econometrics, 1, 26-27 (in Russian).
Balatsky E. (2005). Factors of Life Satisfaction: Measurement and Evaluation. Monitoring of Public Opinion, 4, (76), 44-48 (in Russian).
Davydov A. (1995). Index of social disadvantage. Sociological research, 10, 118-128 (in Russian).
Desai M. (2002). Marx's Revenge: The Resurgence of Capitalism and the Death of Statist Socialism. London: Verso.
Dzolo D. (2010). Democracy and Complexity: A Realistic Approach. Moscow: NRU - HSE (in Russian).
Gavrilets Y., Klimenko K., Kudrov A. (2016). Statistical analysis of the social tension factors in Russia. Economics and Mathematical Methods, 1, 90-111 (in Russian).
Gavrilets Y., Nikitin S., Chernenkov M. (2018). Population's Assessment of the Life Quality and Social Stability in the Regions of Russia. Moscow: Applied Mathematics Institute (in Russian).
Hagerty M.R., Cummins R.A., Ferriss A.L., Land K., Michalos A.C., Peterson M. et al. (2001). Quality of Life Indexes for National Policy. Davis: Graduate School of Management University of California.
Ivanova E. (2017). Rating of Russian Regions by Level of the Life Quality. Available at: (accessed: June 2018, in Russian).
Liga M. (2006). Life Quality as a Basis of Social Security. Moscow: Gardariki (in Russian).
Luhmann N. (2007). Social Systems. Saint Petersburg: Nauka (in Russian).
Maslow A. (1999). Motivation and Personality. Saint Petersburg: Evrazija (in Russian).
Measuring Human Development Index: The Old, the New and the Elegant. Indira Gandhi Institute of Development Research, Mumbai October 2013. Available at: (accessed: June 2018).
Osipov G. (2002). Sociology and Social Myth Creation. Moscow: Norma-Infra-M (in Russian).
Rimashevskaya M., Bochkareva V., Volkova G., Korchagina L. (2012). Regional Features of the Level and Quality of Life. Moscow: ISEPI RAN, "M-Studio" (in Russian).
Sen A. (2010). The Idea of Justice. London: Penguin Books Ltd.
Volkova M. (2010). Comparison of Objectivist and Subjectivist Approaches to Measuring Synthetic Latent Categories of the Life Quality: Results of Empirical Analysis of Russian Data. . Applied Econometrics, 3, 62-90 (in Russian).
Zaslavskaya T. (2004). Modern Russian Society. Social Mechanism of Transformation. Moscow: Delo (in Russian).

Morozov S.L. Standard 13-month reference calendar Medler-Mendeleev-Morozov Standard in space society
Economics and mathematical methods
, 2019, 55 (1), 116-125.

      Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia;

Abstract. Space society is in the sixth socio-economic formation of Civilization. There are two fundamentally different points of view on Space ideology: 1) geocentric (from Earth to Space); 2) cosmocentric or astrocentric (from Space to Earth). The sixth socio-economic formation (Space) is cosmocentric and is different from the previous five, (purely terrestrial, geocentric) socio-economic formations (primitive community, slave, feudal, capitalist and socialist (communist)). The challenge is to look at the Earth from Space as one of the many spaceships of Civilization and perceive the Earth as a normal part of the nature of Space (cosmocentrizm). Landmarks for astronauts in space will be 88 constellations, not the gods of ancient Egypt, Greece and Rome. In Space there is no earthly top, no bottom, no day, no night, no seasons, no equinoxes, no solstices, no different-day months of the year, no phases of the moon. In Space, in particular, does not make any sense none of the approximately ? 40 existing today medieval geocentric clerical terrestrial analog elliptical calendars. For the names of the months they have the names of the ancient Roman and Greek gods and goddesses. For the purposes of astronavigation and astrodynamics in Space, they are completely useless. Therefore, NASA (USA) for the purposes of exclusively astronavigation and astrodynamics, introduced the 13th zodiac Serpentarius (Ophiuchus-Apheuhus) calendar system from January 13, 2016 and openly announced it. The Space society will have a standard 13-month reference mathematical calendar of the year, focused on 88 major constellations of the Universe listed in the Star catalog of 1928, of which 13 zodiac constellations are on the Ecliptic of the Sun. This calendar will show a single time in all the spaceships of Humanity in the Universe, including Earth as one such spaceship. The article presents the fundamental principles of the mathematical standard 13-month reference zodiac calendar.
Keywords: standard 13-month reference calendar of Medler-Mendeleev-Morozov; singular point of time "January 1, 2013 (2013-I-01 00:00:00.000000000)", lag error in the time code ISO 8601, Space society, sixth socio-economic structure, geocentrism, cosmocentrizm, astrocentrism, single time, space ships, Universe; the space society industrialization.
JEL Classification: C60, F55, F59.
DOI: 10.31857/S042473880003983-0

      REFERENCES (with English translation or transliteration)
Morozov S.L. (2013). About One New Calendar System. Economics and Mathematical Methods, 49, 4, 111-125 (in Russian).
Morozov S.L. (2018a). The Homeostatic Ark and the Standard Permanent Calendar of D. I. Mendeleev as the Main Means in the Strategy of Industrialization of Space and Creation of Space Society [Gomeostaticheskij kovcheg i etalonnyj postoyannyj kalendarj D.I. Mendeleeva kak glavnye sredstva v strategii industrializatsii cosmosa I sozdaniya cosmicheskogo obshchestva]. Monographiya. Moscow: Vash Format (in Russian).
Morozov S.L. (2018b). The Mendeleevsky Standard Calendar of Russia for 2019. Monography. Moscow: Vash Format (in Russian).
Morozov S.L. (2018). The Mendeleevsky Standard Calendar of Russia for 2020. Monography. Moscow: Vash Format (in Russian).
Sukhova S. (2018). The Standard of the Year Was Not, and Is Not. The Economist Explained Svetlana Sukhova, Which Calendar Needs of Modern Humanity? [Etalona goda kak ne bylo, tak I net. Economist objyasnil Svetlane Sukhovoj, kakoj kalendarj nuzhen sovremennomu chelovechestvu?]. Ogonek, 49 (5544), 26-27 (in Russian).


Vol. 55, No. 2

Akhmadeev B.A.*, Makarov V.L.** Project assessment system based on combined methods of computer optimization
Economics and mathematical methods
, 2019, 55 (2), 5-23.

      Central Economics and Mathematics Institute, Russian Academy of Sciences
      * E-mail:
      ** E-mail:

Abstract. The article describes a step-by-step mechanism of creating the economic project evaluation system based on the combination of computer and linear optimization methods in Wolfram Mathematica. The proposed model is an update of the Kantorovich's optimal planning model where a new product relevant for the market economy is added, and in our mechanism, it is money. Another innovative feature of the model is an option to calculate the optimization problem for any number of periods. An optimization method for public investments into projects proposed; it is based on the automatic analysis of "shadow prices" of the linear programming dual problem. A range of experiments are carried, which by means of the graphics illustrate, how various optimization criteria may influence the solution and what consequences they may have in various aspects of the concerned economic environment. For example, if the goal of the regional administration is to increase the financial well-being of the population, then the wage vector is maximized. If the goal of the regional authorities is to increase the profit of any industry or enterprise, then the corresponding vector is maximized. There are many purposes, so the optimization criterion can be combined with different weights corresponding to the tasks facing management. The developed system may be included in the network of situation centers to optimize management solutions at the level of major industrial enterprises, regions or the whole of the country.
Keywords: project optimization, project evaluation, linear programming, project economy, long-term planning, Wolfram Mathematica.
JEL Classification: C61, C63, O21, G31.
DOI: 10.31857/S042473880003315-5

      REFERENCES (with English translation or transliteration)
Akhmadeev B., Manakhov S. (2015) Effective and Sustainable Cooperation between Start-ups, Venture Investors, and Corporations. Journal of Security and Sustainability, 5 (2), 269-285. DOI:
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Kantorovich L.V. (1959). Economic Calculation of the Best Use of Resources. Moscow: Publishing House of the USSR Academy of Sciences (in Russian).
Kantorovich L.V., Bogachev V.N., Makarov V.L. (1970). About an Estimation of Efficiency of Capital Expenses. Economics and Math. Methods, 6, 6, 811-826 (in Russian).
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Skrypnik D.V. Budget policy and economic growth in Russia. Optimal budget rule
Economics and mathematical methods
, 2019, 55 (2), 24-40.

      Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia;
Sections 1-3 of this study got financial support from the Russian Foundation for Basic Research (project 17-02-00524-).

Abstract. The work was carried under the scientific supervision of RAS Academician, Doct. Sc. (Economics) V.M. Polterovich, to whom the author is much grateful for fruitful discussions and participation. Author expresses his gratitude to Doct. Sc. (Economics) M.Yu. Afanas'ev and Correspondent member RAS M.Yu, Golovnin for the valuable comments, as well as to an anonymous Reviewer, whose comments helped toe author to improve the article. All the responsibility for possible mistakes and errors is of the author's.
The article shows that actual public expenditure in the period of rapid oil prices growth of the 2000s was less than the optimal level in Russia. The macroeconomic model of Russian economy is the basis of current research. The main mechanism of growth in an optimum scenario is associated with the scaling effect of public expenditure, which increases production possibilities of an economy. Adequate monetary policy allows preventing unwinding of the inflation spiral and runs the growth spiral. Non-optimality of fiscal policy is a consequence of budget rule mechanism features, which do not take into account the influence of government expenditures on economic growth. The fiscal rule that implements the "closed loop" control and allows constructing the optimal economic policies for developing countries can become a basis for the system of growth management that combines universal and program planning. The key principle of optimal budget rule must be "t?tonnement" like process of budget parameters choice.
Keywords: optimal control, macroeconomic model, fiscal rule.
JEL Classification: E620, O230, H540, 510, 520, 320.
DOI: 10.31857/S042473880004675-1

      REFERENCES (with English translation or transliteration)
Berg A., Portillo R, Yang S., Zanna L.F. (2012). Public Investment in Resource Abundant Low-Income Countries. IMF/CBRT Conference on Policy Responses to Commodity Price Movements. Istanbul.
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Glazev S.Yu. (2006). "Kudryavaya" economika. Politicheskiyi Jurnal. 43-44, 47-48, 24-25 (in Russian).
Gurvich E., Vakulenko E., Krivenko P. (2009). Cyclical Properties of Fiscal Policy in Oil-Producing Countries. Voprosy Ekonomiki, 2, 51-70 (in Russian).
Gurvich E.T. (2006). Fiscal and Monetary Policy in an Unstable External Environment. Voprosy Ekonomiki, 3, 4-27 (in Russian).
Idrisov G.I., Sinelnikov-Murylev S.G. (2013). Budget Policy and Economic Growth. Voprosy Ekonomiki, 8, 35-59 (in Russian).
Kudrin A.L., Knobel A.Y. (2010). Fiscal Policy as a Source of Economic Growth. Voprosy Ekonomiki, 10, 5-26 (in Russian).
Polterovich V.M. (2015). On the Formation of National Planning System in Russia. Journal of the New Economic Association, 2 (26), 237 (in Russian).
Skrypnik D.V. (2016). A Macroeconomic Model of the Russian Economy. Economics and the Mathematical Methods, 52, 3, 92-113 (in Russian).
Solntsev O.G., Belousov D.R. (2005). The Use of Stabilization Fund's Resources for Economic Growth Stimulating. Studies on Russian Economic Development, 4, 21-27 (in Russian).
Strategy for the modernization of the Russian economy (2010). Polterovich V.M. (ed.). Saint Petersburg: Aleteija (in Russian).

Repina E.G.i,*, Shiryaeva L.K.i,**, Fedorova E.A.ii,*** The study of dependence structure between small business development and microfinance security of Russian regions
Economics and mathematical methods
, 2019, 55 (2), 41-57.

      i Samara State University of Economics, Samara, Russia
      ii Financial University under the government of the Russian Federation, Higher school of Economics, Moscow, Russia
      * E-mail:
      ** E-mail:

Abstract. The hypothesis about the change of dependence structure between the level of the small business (SB) development and security of the regional microfinance institutions (MFIs) in connection with the state regulation of MFI activities in 2013-2016 is advanced. The level of small business development and microfinance security of Russian regions are described by the number of small business enterprises and the number of registered MFIs per 1,000 people population of the region. The dependence structure is modeled using the copula-function method. The selection of a suitable copula is based on minimizing the AIC information criterion. The goodness of fit of the copula is hecked by means a test based on Cramer-von Mises statistics. The probabilistic structure of the dependency between the MFIs security and the SB level in the period 2012-2016 has transformed from independence copula in 2012-2013 to Frank's copula in 2014-2015 and Clayton's copula in 2016. It is concluded that the transformations of the probabilistic structure of the studied dependence in 2012-2016 are explained to the long-time effect because of the state regulation measures of the MFI sphere in 2013-2016. The novelty of the work lies in assessing the impact of state regulation measures in the field of MFIs on the level of small business development in the regions based on the copula-function method.
Keywords: microfinance organizations, small business, copula-function method, independent copula, Archimedean copulas, maximal likelihood method, tail dependencies, AIC information criterion, Cramer-von Mises statistics.
JEL Classification: C52, E58, G21, O160.
DOI: 10.31857/S042473880004680-7

      REFERENCES (with English translation or transliteration)
Babajide A. (2012). Effects of Microfinance on Micro and Small Enterprises (MSEs) Growth in Nigeria. Asian Economic and Financial Review, 2, 463-477.
Balakrishnan N., Lai C.-D. (2009). Continuous Bivariate Distributions. New York: Springer.
Baydas M. (1994). Credit Rationing in Small Scale Enterprises: Special Microenterprise Programs in Ecuador. Journal of Development Studies, 31 (2), 279-308.
Baydas M. (2004). Market Assessment for Housing Microfinance. In: Daphis F., Ferguson B. (eds) "Housing Microfinance: A Guide to Practice". Bloomfield: Kumarian Press.
Belousov A.L. (2015). The Regulation of Microfinance Institutions: Problems and Prospects. Finances and Credit, 26 (650), 39-46 (in Russian).
Bouye E. (2002). Multivariate Extremes at Work for Portfolio Risk Measurement. Finance, 23 (2), 125-144.
Breymann W., Dias A., Embrechts P. (2003). Dependence Structures for Multivariate High-Frequency Data in Finance. Quantitative Finance, 3, 1-14.
Burdun G.D., Markov B.N. (1985). Basics of Metrology. Moscow: Publishing House of Standards (in Russian).
Collins D., Morduch J., Rutherford S., Ruthven O. (2009). Portfolios of the Poor: How the World's Poor Live on $2 a Day. Princeton: Princeton University Press.
Dichter T., Harper M. (2007). What's Wrong with Microfinance? Warwickshire: Practical Action Publishing.
Fantazini D. (2011c). Modeling Multidimensional Distributions Using Copula Functions. III. Applied econometrics, 4 (24), 100-130 (in Russian).
Fantazini D. (2011a). Modeling Multidimensional Distributions Using Copula Functions. I. Applied econometrics, 2 (22), 98-134 (in Russian).
Fantazini D. (2011b). Modeling Multidimensional Distributions Using Copula Functions. II. Applied econometrics, 3 (23), 98-132 (in Russian).
Genest C., R?millard B., Beaudoin D. (2009). Goodness-of-Fit Tests for Copulas: A Review and Power Study. Insurance: Mathematics and Economics, 44 (2), 199-213.
Guerin I., Labie M., Servet J.-M. (2015). The Crises of Microcredit. New York: Zed Books.
Karpushin E.S. (2016). Development of the Market for Microfinance Organizations in Russia: Conflict of Interests of Investors, Borrowers and the State. Issues of Economics, 9, 150-158 (in Russian).
Kendall M., Stuart A. (1973). Statistical Findings and Links. Moscow: Nauka (in Russian).
Khandker S.R. (2005). Microfinance and Poverty: Evidence Using Panel Data from Bangladesh. The World Bank Economic Review, 19, 263-286.
Kovaleva E.A. (2011). Microfinance is a New Tool for Small Business Development. Economic science, 74, 271-274 (in Russian).
Ledgerwood J., White V. (2006). Transforming Microfinance Institutions: Providing Full Financial Services to the Poor. Washington: World Bank.
Lemeshko B.Yu., Chimitova E.V. (2003). On the Choice of the Number of Intervals in the Criteria of Type Agreement. Factory Laboratory. Diagnostics of Materials, 69, 61-67 (in Russian).
Nelsen R.B. (2006). An Introduction to Copulas. Lecture Notes in Statistics. New York: Springer-Verlag.
Ngoasong M.Z., Kimbu A.N. (2016). Informal Microfinance Institutions and Development-led Tourism Entrepreneurship. Tourism Management, 52, 430-439.
Rozanova L.I. (2015). Microfinance Organizations in the Regional Market: Usurers or Investors. Finance and Credit, 30 (654), 40-47 (in Russian).
Semin R.N. (2007). Development of the Institutional Environment: Financial Support of Small Business. Digest Finance, 13(149), 31-38 (in Russian).
Shahnazaryan G.E. (2016). Comparative Analysis of the Legal Regulation of the Activities of Commercial Microfinance Institutions in the Countries of the Eurasian Economic Union. Finance and Credit, 12 (684), 24-39 (in Russian).
Sklar A. (1959). Fonctions de r?partition ? n dimensions et leurs marges. Publications de l'Institut de Statistique de L'Universit? de Paris, 8, 229-231.
Tucker M., Miles G. (2004). Financial Performance of Microfinance Institutions: A Comparison to Performance of Regional Commercial Banks by Geographic Regions. Journal of Microfinance/ ESR Review, 6 (1), 41-54.
Woolcock M. (1999). Learning from Failures in Microfinance: What Unsuccessful Cases Tell Us How Group Based Programs Work. American Journal of Economics and Sociology, 58 (1), 17-42.

Assaul V.N.*, Pogodin I.E.** On the transportation problem with ecological criterion
Economics and mathematical methods
, 2019, 55 (2), 58-64.

      Naval Polytechnic Institute, Saint Petersburg, Russia
      * E-mail:
      ** E-mail:
The authors are grateful to I.A. Barsuk for creating the conditions for the necessary calculations performing, A.I. Popova for help in design, as well as R.I. Musatenko for the idea of an environmental approach.

Abstract. Three ways of solving the transport problem are considered, in which, in addition to the transportation fee of each unit of cargo, a fixed fee for the use of a particular route by each carrier is additionally charged regardless of the amount of cargo carried on it. (1) With the help of a detailed logical analysis of a payment matrix with a decision tree construction that takes into account corrective cycles, at the same time, deliveries to all unfilled cells are considered, and those which lead to the objective function decreasing are selected. (2) With the choice of the best plan from the set of iterative variants, in each the costs of transport along the used routes (cells) are replaced by actual ones. That means it is recalculated taking into account the additions to the initial costs of transportation the "penal additives", reduced to a unit of cargo transported along the corresponding route at the previous iteration. (3) With the approximate reduction of two-component costs to the effective continuous values of unit transportation costs, that simulates the stepwise contribution of additional payments, and the further reduction of the problem to the search of extremum to a function of several variables. Estimates are made of the conditions under which the task necessarily requires accounting for additional payments on the routes. Since the very formulation of the problem did not have a single term for it, taking into account current conditions, the term "transport problem with ecological criterion" was proposed.
Keywords: objective function, transportation cost, optimal plan, corrective cycle.
JEL Classification: C02, C44, C54, C65.
DOI: 10.31857/S042473880003951-5

      REFERENCES (with English translation or transliteration)
Balinski M.L. (1961). Fixed Cost Transportation Problem. Naval Res. Log. Quart, 8, 1, 41-54.
Birman I.Ya. (1968). Optimal Programming. Moscow: Ekonomika (in Russian).
Frolkis V.A. (2002). Introduction to the Theory and Optimization Methods for Economists. Saint Petersburg: Peter (in Russian).
Kantorovich L.V. (1942). On the Movement of Masses. Reports of the USSR Academy of Sciences, 37, 227-229 (in Russian).
Korbut A.A., Finkelstein Yu.Yu. (1969). Discrete Programming. Moscow: Nauka (in Russian).
Polyak R.A. (1966). On one Inhomogeneous Transport Problem. In: "Mathematical Models and Methods of Optimal Planning". Novosibirsk: Nauka, 109-115 (in Russian).
Sedova S.V., Lebedev S.S. (1999). The Decision of One Task of Placement with Use of Nodal Vectors of the Resolving Multipliers. Economy and Mathematical Methods, 35, 3, 116-121 (in Russian).
Sedova S.V., Lebedev S.S. (2001). Method of Nodal Vectors of Integer Programming. Problems of a Special Look. EMI preprint. WP/2000/094 (in Russian).
Sigal I.Kh., Ivanova A.P. (2007). Introduction to Applied and Discrete Programming: Models and Computational Algorithms. Moscow: Fizmatlit, 45-49 (in Russian).
Tui H. (1964). Concave Programming with Linear Constraints. Reports of the Academy of Sciences of the USSR, 159, 1, 32-35 (in Russian).

Aivazian S.A., Bereznyatskiy A.N.*, Brodsky B.E.** Non-equilibrium structural models of the real sector of the Russian economy
Economics and mathematical methods
, 2019, 55 (2), 65-80.

      Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia
      * E-mail:
      ** E-mail:
This study was financially supported by the Russian Science Foundation (project 17-18-01080).

Abstract. This paper aims at description of prospects of the Russian economy in the middle-term scenario, when changes of the drivers of the economic growth are possible. How and due to which factors the Russian economy will go out the world economic crisis of 2019, what is the role of the economic policy in this situation? In this paper we consider a macroeconomic model created upon the main ideas of the structural modeling, which enables us to describe the main trajectories of economic development in different scenarios. In its essence this model disaggregates the sphere of the real production of the Russian economy into the following sectors: E.O.M. (export-oriented markets), D.O.M. (domestic-oriented markets), N.M. (natural monopolies). Interactions between these sectors are reflected of the final form of the model: the system of two first difference equations describes dynamics of the output in E.O.M. and D.O.M. sectors. Since the dynamics of output in the N.M. sector is determined from the outputs of E.O.M. and D.O.M. sectors and the total output of the Russian economy depends on the total output of the real sector, we can consider the aggregated values in subsequent stages of econometric modeling. With account of conjuncture factors revealed by theoretical analysis, we create the macroeconometric model, which gives estimates of price indicators and production indices in the main branches of the real sector. The novelty of the proposed approach to applied macroeconomic modeling of the Russian economy, thus, consists in taking into account the inner structure of the Russian economy, on the one hand, and the specific methodology of modeling for description of nonstationary transitional dynamics of the real data, on the other. In this manner, we arrive at the stage of econometric modeling, where the method of cointegration analysis of Engle-Granger is used.
Keywords: economy of Russia; structural modeling; disaggregated macromodel, applied econometric analysis.
JEL Classification: C30, C32, C51, E13.
DOI: 10.31857/S042473880004674-0

      REFERENCES (with English translation or transliteration)
Aivazian S.A., Bereznyatskiy A.N., Brodsky B.E. (2017). Macroeconomic Modeling of the Russian Economy. Applied Econometrics, 47, 5-27.
Aivazian S.A., Enjukov I.S., Meshalkin L.D. (1985). Applied Statistics. Study of Relationships. Moscow: Finansy i statistika (in Russian).
Colander D., Howitt P., Kirman A., Leijonhufved A., Mehrling P. (2008). Beyond DGSE Models. Toward an Empirically Based Macroeconomics. American Economic Review. Papers and Proceedings, 98 (2), 236-240.
Colander D. (2010). Testimony Presented to U.S. House of Representatives Science and Technology Committee Hearing Entitled "Building a Science of Economics for the Real World". Serial No. 111-106, July 20.
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Davidson R., MacKinnon J.G. (1993). Estimation and Inference in Econometrics. New York: Oxford University Press.
Edge R., Gurkaynak R. (2011). How Useful are Estimated DSGE Model Forecasts for Central Banks? Brookings Papers on Economic Activity, Fall 2010.
Engle R.F., Granger C.W.J. (1987). Cointegration and Error Correction: Representation, Estimation and Testing. Econometrica, 55, 251-276.
Fair R.C. (2004). Estimating How the Macroeconomy Works. Cambridge: Harvard University Press.
Fair R.C. (2007). Evaluating Inflation Targeting Using a Macroeconomic Model, Economics. The Open Access Journal, 1-52, 2007-2008.
Fernandez-Villaverde J. (2010). The Econometrics of DSGE Models. Journal of the Spanish Economic Association, 1, 3-49.
Granger C.W.J., Newbold P. (1974). Spurious Regressions in Econometrics. Journal of Econometrics, 35, 143-159.
Heim J. (2017). An Econometric Model of the US Economy. London: Palgrave-MacMillan.
Klein L., Welfe A., Welfe W. (1999). Principles of macroeconometric modeling. Advanced textbooks in economics, 36. Elsevier.
Klein L., Evans M. (1968). The Wharton Econometric Forecasting Model. Wharton School of Finance and Commerce. Philadelphia: University of Pennsylvania.
Mankiw N.G. (2006). The Macroeconomist as Scientist and Engineer. Journal of Economic Perspectives, 20 (4), 29-46.
Paccagnini A. (2011). DSGE Model Evaluation and Hybrid Models: A Comparison. European University. Working paper, 2011/11.
Sims C. (1972). Money, Income, and Causality. The American Economic Review, 62 (4), 540-552.
Sims C. (1980). Macroeconomics and Reality. Econometrica, 48 (1), 1-48.
Smets F., Wouters R. (2003). An Estimated Dynamic General Equilibrium Model of the Euro Area. Journal of the European Economic Association, 1 (5), 1123-1175.
Solow R.M. (2010). Testimony Presented to U.S. House of Representatives Science and Technology Committee Hearing Entitled "Building a Science of Economics for the Real World". Serial No. 111-106, July 20.
Welfe W. (2013). Macroeconometric models. Advanced studies in theoretical and applied econometrics, 47. Springer.

Svetlov K.V. Herding behaviour on stock market: analysis and forecasting
Economics and mathematical methods
, 2019, 55 (2), 81-97.

      Bank 'Saint-Petersburg' PJSC, Saint-Petersburg, Russia E-mail:
Received 20.11.2017 .

Abstract. This study was supported by the Russian Foundation for Basic Research (project 15-06-05625-a) "Consumer choice and herding behaviour in microeconomics: from analytical description towards realistic agent-based models".
The author is grateful to the project manager - dr. D.V. Kovalevsky for helpful comments. The organization providing the conditions for the project implementation is the Scientific Foundation "Nansen International Enviromental and Remote Sensing Centre" (Foundation Nansen-Centre, St. Petersburg).
We study the Alfarano model, which describes the dynamics of the stock price under the influence of the herding behavior of market participants. Within the framework of this model, two types of economic agents are distinguished: investors and noise traders. It is assumed that among traders there are optimistic traders expecting price value to rise and pessimistic traders expecting it to decline. The stochastic nature of the price in this model is formed by the changes of noise traders expectations. Unlike other stochastic models of price dynamics the price obtained within the framework of this model is bounded, while its boundaries are determined by the parameter of the market sensitivity to the changes of traders expectations. Using the diffusion approximation for the Markov process describing the ratio of numbers of optimistic and pessimistic traders, we analyze this model. Depending on the input parameters, we study such aspects of this model as the possibility of reaching price boundaries, when absolutely all traders have optimistic or pessimistic expectations. The main objective of the work is to build a forecast for future price values, including their long term asypthotics, as well as to derive the formulas for determining the value of derivatives (such as european call option) and to investigate the possibility of their hedging.
Keywords: herding behavior, stochastic dynamics, option pricing.
JEL Classification: C63, G13.
DOI: 10.31857/S042473880003987-4

      REFERENCES (with English translation or transliteration)
Abramowitz M., Stegun I. (eds) (1965). Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables (Vol. 55). New York: Dover Publications Inc.
Alfarano S., Lux T., Wagner F. (2008). Time Variation of Higher Moments in a Financial Market with Heterogeneous Agents: An Analytical Approach. Journal of Economic Dynamics and Control, 32, 1, 101-136.
Bhattacharya R.N., Waymire E.C. (2009). Stochastic Processes with Applications. In: "Society for Industrial and Applied Mathematics". Berlin: Springer Berlin Heidelberg.
Bjork T. (2010). Arbitrage Theory in Continuous Time. Moscow: Lan'. [Bjork T. (2009). Arbitrage Theory in Continuous Time. New York: Oxford University Press.]
Borodin A.N. (2013). Random Processes. Saint-Petersburg: Lan' (In Russian).
Cont R., Bouchaud J.P. (2000). Herd Behavior and Aggregate Fluctuations in Financial Markets. Macroeconomic Dynamics, 4, 2, 170-196.
Delbaen F., Shirakawa H. (2002). An Interest Rate Model with upper and Lower Bounds. Asia-Pacific Financial Markets, 9, 3, 191-209.
Ekstr?m E., Tysk J. (2011). Boundary Conditions for the Single-Factor Term Structure Equation. The Annals of Applied Probability, 21, 1, 332-350.
Follmer H., Schweizer M. (1993). A Microeconomic Approach to Diffusion Models for Stock Prices. Mathematical Finance, 3, 1, 1-23.
Gihman I.I., Skorohod A.V. (1979). The Theory of Stochastic Processes III. New York: Springer New York.
Karlin S., Taylor H.E. (1981). A Second Course in Stochastic Processes. New York: Academic Press.
Kirman A. (1993). Ants, Rationality, and Recruitment. The Quarterly Journal of Economics, 108, 1, 137-156.
Kovalevsky D.V. (2016). Modeling Herding Behavior on Financial Markets Affected by Exogenous Climate-Related Shocks. The 8th International Congress on Environmental Modelling and Software (iEMSs 2016), 10-14 July 2016, Toulouse, France. Available at: httpsredir=1 article=1586 context=iemssconference (accessed: November 2017).
Oksendal B. (2003). Stochastic Differential Equations: An Introduction with Applications. Berlin: Springer Berlin Heidelberg.

Tomashevskii I.L.i,*, Aksenov V.V.ii,** How the irrational marketing strategy might lead to economic success: a mathematical modeling taking into account behavioral factors
Economics and mathematical methods
, 2019, 55 (2), 98-103.

      i Northern (Arctic) Federal University, Higher School of Information Technologies and Automation Systems, Arkhangelsk, Russia
      ii Higher School of Engineering, Arkhangelsk, Russia
      * E-mail:
      ** E-mail:

Abstract. Behavioral economics is one of the most rapidly developing branches of economic science. It captures the profound influence of psychological factors on the development of economic processes and helps to understand the impact of human psychology on economic decision-making. In this paper, there is a model of enterprise development, supplying ordinary everyday consumer goods to the markets. The model takes into account the main behavioral factors determining the demand of goods: initial advertising, mismatch of demand with supply and the "word of mouth" advertising, as well as the economic policy of the manufacturer. It is shown that the "sluggish" reaction of the manufacturer to the changing situation in the consumer market opens up options to act psychological factors and leads to effective economic development of the manufacturer. Conversely, strict control of market situations and actions, that seem economically justified, can "drown out" behavioral factors and lead to economic stagnation or decline. The model is formulated in terms of differential equations.
Keywords: behavioral economics, economic modelling, mathematical modelling in economics.
JEL Classification: D03, D04, E03.
DOI: 10.31857/S042473880004024-5

      REFERENCES (with English translation or transliteration)
Ball R.J. (2017). Inflation and the Theory of Money. New York: Routledge.
Berger J. (2014). Word of Mouth and Interpersonal Communication: A Review and Directions for Future Research. Journal of Consumer Psychology, 24, 586-607.
Debreu G. (1974). Excess-Demand Functions. Journal of Mathematical Economics, 1, 15-21.
DeGraba P. (1995). Buying Frenzies and Seller-Induced Excess Demand. The RAND Journal of Economics, 26, 331-342.
Gisser M. (2009). Some Anomalies Arising from Bandwagons that Impart Upward Sloping Segments to Market Demand. Econ Journal Watch, 6, 21-34.
Lang B., Hyde K. (2013). Word of Mouth: What We Know and What We Have Yet to Learn. Journal of Consumer Satisfaction, Dissatisfaction and Complaining Behaviour, 26, 1-18.
Leibenstein H. (1950). Bandwagon, Snob, and Veblen Effects in the Theory of Consumers' Demand. Quarterly Journal of Economics, 64, 183-207.
Mantel R. (1974). On the Characterization of Aggregate Excess-Demand. Journal of Economic Theory, 7, 348-353.
Sernovitz A. (2012). Word of Mouth Marketing: How Smart Companies Get People Talking. Austin: Greenleaf Book Group Press.
Van Herper E., Pietars R., Zeelenberg M. (2009). When Demand Accelerates Demand: Trailing the Bandwagon Van. Journal of Consumer Psychology, 302-312.

Borovkova A.E. Product differentiation in two-sided market with uncertainty in product quality value
Economics and mathematical methods
, 2019, 55 (2), 104-117.

      Lomonosov Moscow State University, Moscow, Russia

Abstract. In this paper we present the two-sided model of the firms' behavior with product versioning. We find the influence on groups of agents' demand, on product price for each group and on platform profit of such factors as network effect, the quality of test version of platform and agents expectations about platform quality before purchase. The methods of microeconomics, industrial economics, game theory and contract theory are used. The main conclusions confirm the benefit from versioning to a firm in case of strong indirect network effects in the market between two groups of agents. Additional opportunity to increase platform quality after purchase also affects positively on the firm's profit in comparison to the strategy to produce only one version or the decision to supply two modifications without permission to change one for another. Presented results develop the existing literature on the two-sided platforms.
Keywords: two-sided platforms, market with network effects, platform, indirect network effect, versioning.
JEL Classification: L10, L21, L22, M21.
DOI: 10.31857/S042473880004681-8

      REFERENCES (with English translation or transliteration)
Aloui Ch., Jebsi K. (2010). Optimal Pricing of a Two-Sided Monopoly Platform with One-Sided Congestion Effect. International Review of Economics, 57 (4), 423-439.
Armstrong M. (2006). Competition in Two-Sided Markets. RAND Journal of Economics, 37 (3), 668-691.
Belleflamme P. (2005). Versioning in the Information Economy: Theory and Applications. CESifo Economic Studies, 51, 2-3, 329-358.
Belleflamme P., Peits M. (2010). Industrial Organization. Markets and Strategies. Cambridge: Cambridge University Press.
Bhargava H.K., Choudhary V. (2001). Information Goods and Vertical Differentiation. Journal of Management Information Systems, 18 (2), 89-106.
Bhargava H. K., Choudhary V. (2008). Research Note: When is Versioning Optimal for Information Goods? Management Science, 54 (5), 1029-1035.
Blagov .Yu. (2012). Mathematical Models of the Dynamics of Multilateral Network Platforms. Problems of Modern Economics 4, 44, 149-152 (in Russian).
Economides N., Tag J. (2012). Network Neutrality on the Internet: A Two-sided Market Analysis. Information Economics and Policy, 24, 91-104.
Gabszewicz J.J., Wauthy X.Y. (2004). Two-Sided Markets and Price Competition with Multi-Homing. CORE Discussion Paper No. 2004/30. Louvain-la-Neuve, Belgium.
Gabszewicz J.J., Wauthy X.Y. (2012). Platform Competition and Vertical Differentiation. CORE Discussion Paper. Universit? Catholique de Louvain. Center for Operations Research and Econometrics.
Global Top 100 Companies by market capitalization (2017). Available at: (accessed: March 2018).
Hagiu A. (2007). Merchant or Two-Sided Platform? Review of Network Economics, 6 (2), 115-133.
Hagiu A., Spulber D. (2013). First-Party Content and Coordination in Two-Sided Markets. Management Science, 59 (4), 933-949.
Hagui A., Halaburda H. (2013). Expectations and Two-sided Platform Profits. Harvard Business School. Working Paper No. 12-045.
Hagui A., Halaburda H. (2014). Information and Two-sided Platform Profits. Harvard Business School. Working Paper No. 12-045.
Kovalenko A.I. (2016). Multisided Platforms Research Problematic. Journal of Modern Competition, 10, 3 (57), 64-90 (in Russian).
Nault B.R., Wei X. (2005). Product Differentiation and Market Segmentation of Information Goods. Haskayne School of Business. Working Paper.
Nault B.R., Wei X. (2013). Experience Information Goods: "Version-to-Upgrade". Decision Support Systems, 56, 494-501.
Parshina E.N., Shastitko A.Ye. (2016). Two-Sided Markets: The Subject Matter Specification. Journal of Modern Competition, 10, 1 (55), 5-18 (in Russian).
Rochet J.Ch., Tirole J. (2003). Platform Competition in Two-sided Markets. Journal of the European Economic Association, 1, 990-1029.
Rochet J.Ch., Tirole J. (2006). Two-Sided Markets: A Progress Report. RAND Journal of Economics, 37 (3), 645-667.
Roson R. (2005). Two-Sided Markets: A Tentative Survey. Review of Network Economics, 4 (2), 1-19.
Rysman M. (2009). The Economics of Two-Sided Markets. Journal of Economic Perspective, 23 (3), 125-143.
Shapiro C., Varian H.R. (1998). Versioning: The Smartest Way to Sell Information. Harvard Business Review, 76 (6), 106-114.
Shapiro C., Varian H.R. (1999). Information Rules: A Strategic Guide to the Network Economy. Harvard Business School Press. Boston. Massachusetts.
Shivendu S., Zhang Zh. (2012). Versioning Strategy of Information Goods with Network Externality in the Presence of Piracy. In: "45th Hawaii International Conference on System Science (HICSS)", January.

Grigoryev R.A. Contemporaneous effects of non-synchronous time series: VAR model problems
Economics and mathematical methods
, 2019, 55 (2), 118-129.

      Scientific-Research Institute for Socio-economics development issues in Kazan Innovative University named after V.G. Timiryasov (IEML), Kazan, Russia;
The author is grateful to anonymous reviewers for recommendations on the article improvement. The author is grateful to B.E. Brodskiy for his constructive remarks.

Abstract. Time series data synchronism is not a frequently met condition in theoretical descriptions of econometric models and tests based on them. However, due to the fact that financial institutions are distributed in various time zones, researchers started to use incorrectly the classical econometric models created for synchronous time series in the nonsynchronous data sets. The article critically analyzes the application of nonsynchronous time series in VAR model by Christopher A. Sims as the time series start to demonstrate contemporaneous effects for individual variables, which are absent in the synchronous data sets. The novelty of the work is in revealing the incorrectness of using classical VAR(VECM) model with the set of non-synchronous time series. The usage of time series which values are recorded in different moments inside observation causes the classic models to violate the parity of the initial testing conditions, where one of the series gains advantage in rejecting the Granger causality hypothesis in direction to other series. The presence of such a disparity consists in the fact that the classical model allows contemporaneous effects for the time series recorded later inside observation failing to provide such an opportunity for the opponent time series. A possible way to reduce the effect of disparity lies in the usage of several VAR models. The variable with lag 0 of the time series, the moment which occurs later than that of the opponent's series, in the case of SVAR models leads to the violation of Hume's causality principle. The existence of this variable in the model specification violates the correct assessment of other indicators of the model, while Granger causality for this variable is tested for the direction from the future to the past, which is unacceptable.
Keywords: non-synchronous trading, non-synchronous, VAR, vector autoregression, VECM, contemporaneous term, instantaneous causality, Granger causality.
JEL Classification: 01, 49, 51, 52, 58.
DOI: 10.31857/S042473880004677-3

      REFERENCES (with English translation or transliteration)
Bessler D.A., Yang J. (2003). The Structure of Interdependence in International Stock Markets. Journal of International Money and Finance, 22, 2, 261-287.
Billio M., Caporin M. (2010). Market Linkages, Variance Spillovers, and Correlation Stability: Empirical Evidence of Financial Contagion. Computational Statistics & Data Analysis. 54, 11, 2443-2458.
Brooks C. (2008). Introductory Econometrics for Finance. Cambridge: Cambridge University Press.
Durdyev R., Peresetsky A. (2014). Autocorrelation in the Global Stochastic Trend. Applied Econometrics, 35, 3, 39-58 (in Russian).
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Engle R.F., Granger C.W.J. (1987). Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica: Journal of the Econometric Society, 55, 2, 251-276.
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Kosorukov O.A.i,*, Maslov S.E.ii,**, Semenova N.A.iii,*** Model of determining the moment of the order of delivery with the account of uncertainty of delivery time
Economics and mathematical methods
, 2019, 55 (2), 130-139.

      i Lomonosov Moscow State University, Moscow, Russia
      ii "Prodimex" Ltd., Moscow, Russia
      iii Russian Economic University named after G.V. Plekhanov, Moscow, Russia
      * E-mail:
      ** E-mail:

Abstract. In Russia, most of the trading enterprises in the management of commodity stocks are guided by the average demand and the duration of supply, and only some large companies use the modeling of logistics processes, which increases the efficiency and effectiveness of their operations, reducing the costs of storage and deficit. The article presents a model of inventory management, namely, determining the optimal delivery order moment, taking into account the uncertainty of delivery time. As a criterion of efficiency, a criterion for minimizing integral costs is considered, taking into account the costs of surplus stocks and the costs of the lack of goods in the warehouse. As a law of distribution of a random volume of demand, a triangular distribution is considered, as one of the most applicable under conditions of insufficient statistical data. The considered economic-mathematical model allows to optimize the moment of delivery provided that risks are minimized, based on the statistical data on delivery time for the previous period, or if such data are not available to use expert estimates. These data are sufficient for constructing the probability distribution for a random quantity of demand. The novelty of the work lies in the fact that the model presented in the article allows, with a random delivery time, represented by a triangular distribution, using analytical methods to determine the day of ordering the delivery of a new batch of goods in a certain volume, provided that risks are minimized.
Keywords: inventory management, cost minimization, delivery time, uncertainty of delivery order moment, triangular distribution.
JEL Classification: C61.
DOI: 10.31857/S042473880004685-2

      REFERENCES (with English translation or transliteration)
Anikin B.A., Tyapuhin A.P. (2012). Commercial Logistic. Moscow: Prospekt (in Russian).
Brodezkiy G.L. (2004). Methods of Stochastic Optimization. Mathematical Models of Inventory Management: Textbook. Moscow: REA (in Russian).
Brodezkiy G.L. (2007). Inventory Management. Moscow: Eksmo (in Russian).
Brodezkiy G.L. (2010). System Analysis in Logistic. The Choice under Uncertainty. Moscow: A?k?a?d?e?m?i?ja (in Russian).
Brodezkiy G.L., Gusev D.A. (2012). Economical-Mathematical Methods and Models in Logistics. Optimization Procedures. Moscow: Akademija (in Russian).
Buhvalov V.V., Petrusevich A.V. (2011). Determination of Optimal Production Volumes in the Context of Demand Information Uncertainty. Economics and Mathematical Methods, 47 (2), 3-23 (in Russian).
Dubrov A.M., Lagosha B.A., Khrustalev E.Yu. (2004). Modelling of Risk Situations in Economy and Business. Moscow: Finansy i statistika (in Russian).
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Ivanenco V.I., Labcovskiy V.A. (1990). The Problems of Uncertainty in Decision Making. Kiev: Naukova dumka (in Russian).
Kosorukov O.A. (2016). Optimization Problems of Transportation in Communication Networks with Variable Capacities. Journal of Computer and Systems Sciences International, 55, 6, 1010-1015. DOI: 10.1134/S1064230716060083.
Kosorukov O.A., Maksimov D.A., Shimchenco E.D. (2014). Some Aspects of Demand Modelling in Inventory Management Simulation Models. Logistics, 12, 48-50 (in Russian).
Kosorukov O.A., Maslov S.E. (2018a). Model of Determining Delivery Time with Ucertainty of Demand. Logistics and Supply Chain Management, 4 (87), 45-52 (in Russian).
Kosorukov O.A., Maslov S.E. (2018b). Innovative Methods of Inventory Management under Uncertainty. In: "Innovative Economy and Management: Methods and Technologies". III International scientific-practical conference, Moscow, 16 May 2018, Lomonosov MSU.
Kosorukov O.A., Pechkovskaja V.V., Krasil'nikov S.A. (eds). Moscow: Aspekt Press, 205-208 (in Russian).
Kosorukov O.A., Sviridova O.A. (2009a). Model of Cost Minimization in Inventory Management Systems with Uncertainty of Demand. Logistics and Supply Chain Management, 5 (34), 52-58 (in Russian).
Kosorukov O.A., Sviridova O.A. (2009b). Model of Cost Minimization in Inventory Management Systems. Bulletin of the Russian Economic Academy named after G.V. Plekhanova, 6 (30), 94-102 (in Russian).
Kosorukov O.A., Sviridova O.A. (2012). Stochastic Continuous Model of Inventory Management. Bulletin of the Russian Economic Academy named after G.V. Plekhanova, 4 (46), 91-95 (in Russian).
Kosorukov O.A., Sviridova O.A. (2015). Effective Strategy Formation Models for Inventory Management under the Conditions of Uncertainty. International Education Studies, 8, 5. DOI:
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Vol. 55, No. 3

Nekipelov A.D. Robinson Crusoe model as the starting point for pure economic theory
Economics and mathematical methods
, 2019, 55 (3), 5-20.

      The Moscow School of Economics at Lomonosov State University (MSE MSU), Moscow, Russia; E-mail:

Abstract. In the standard Positive economic science the Robinson Crusoe model is quite widely used as a kind of layout, allowing to illustrate various phenomena and processes typical for a developed market economy - the behavior of isolated producers and consumers, common patterns of economic dynamics, general equilibrium, problems of public finance etc. Pure economic theory is not limited to the task of constructing a set of models, each of which reflects different sides of reality. It is designed to substantiate logically both functional and genetic relationships between the elements of the economic system. The choice of research starting point is of particular importance for this approach as the initial model should, like an embryo, contain the basic characteristics of a developed economic organism in the "minimized form". The article attempts to show that such opportunities are provided by the Robinson Crusoe Model: its analysis allows to introduce in the simplest form many important notions of economic theory, to determine the nature of maximizing behavior of economic agents, to designate the role of space and time in the economy, as well as to lay the groundwork for the next step of economic analysis - identifying the factors contributing to the formation of exchange relations and the social division of labor.
Keywords: pure economic theory, Robinson Crusoe model, maximization of welfare, scarce resources, production program, labor investments, problem of consumer choice, placement of production, uncertainty factor, the theory of the revealed preferences.
JEL Classification: B41, D10, D20, D80, D90, R10.
DOI: 10.31857/S042473880006034-6

      REFERENCES (with English translation or transliteration)
Barro R.J., Sala-i-Martin X. (2004). Economic Growth. Cambridge, London: The MIT Press.
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Nekipelov A. (2006). The Formation and Functioning of Economic Institutions. From "Robinson Crusoe Model" to a Market Economy Based on Individual Production. [Stanovleniye i funktsionirovaniye ekonomicheskikh institutov. Ot "robinzonady" do rynochnoy ekonomiki, osnovannoy na individualnom proizvodstve.]Moscow: Ekonomist" (in Russian).
Nekipelov A. (2017). General Theory of Market Economy. [Obshchaya teoriya rynochnoy ekonomiki.] Moscow: Magistr (in Russian).
Nekipelov A. (2019). The Crisis in Economics - Nature and Ways to Overcome It. [Krizis v ekonomicheskoy nauke - priroda i puti preodoleniya.] Herald of the Russian Academy of Sciences, 89, 1, 24-37 (in Russian).
Pigou A.C. (1932). The Economics of Welfare. London: MacMillan and Co.
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Yoon V.O. Interference of needs and economic decision making
Economics and mathematical methods
, 2019, 55 (3), 21-33.

      Institute of Economic Forecasting, Russian Academy of Sciences, Moscow, Russia; E-mail:

Abstract. Any level of business decisions imply a choice of reaction to current and projected economic events. Not all thoughtful options become real in life, but only those that have successfully passed the mental test of the expediency of implementation. The signal to begin the test is the sense of need, which, starting up the search for economic solutions plays the role of a link between individual consciousness and economy. In contrast to the previous approaches applied to the study of the decision-making process, the author of the article proceeds from non-monotonous nature of the growing need. A wave-like sensation of their urgency is postulated; it allows us to formulate a hypothesis of the needs' interference. It follows that needs can strengthen and weaken each other, depending on the overlapping of their phases. Mutual influence gives probabilistic properties to the resulting action. The solution can be uniquely identified only at the moment of implementation, that is, the process of its adoption occurs according to the quantum world event scheme. The novelty of the article is the approach to the formation of individual economic solution; it is associated with the properties of quantum processes. The set of needs, their phases and the desirability of ways to meet depend on the composition of the environment in which interference occurs. This environment is institutional, and its influence on the decision maker is determined by education, upbringing and experience of decision-making person. The lack of a deterministic connection between motivating influences and economic decisions and the peculiarities of Russian institutions explain the incompatibility of today's typical behavioral priorities with innovative development, as well as the discrepancy between expected and actual results of reforms.
Keywords: decision making, action, need, priorities, virtuality, wavelike oscillation, interference, quantum effects, alignment of marginal utility, motivating environment.
JEL Classification: C0, D8, D9.
DOI: 10.31857/S042473880005786-3

      REFERENCES (with English translation or transliteration)
Avtonomov V.S., Ananyin O.I., Afontsev SA, Gloveli GD, Kapelyushnikov R.I., Makasheva N.A. (2002). History of Economic Thought: Textbook. Manual for University Students. Moscow: Infra-M (in Russian).
Chang H.-J. (2015). Economics: The User's Guide. Moscow: Mann, Ivanov i Ferber (in Russian).
Chernigovskaya T.V. (2013). Schr?dinger's Cheshire Smile: Language and Consciousness. Moscow: Jazyki slavjanskoi kul'tury (in Russian).
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Fukuyama F. (2004). Trust. The Social Virtues and the Creation of Prosperity. Moscow: Ermak (in Russian).
Galin V.V. (2013). The Last Civilization. Moscow: Algoritm (in Russian).
Greenstein G., Zajonc A.G. (2008). The Quantum Challenge. Modern Research on the Foundations of Quantum Mechanics. Dolgoprudnyi: Intellekt (in Russian).
Hidalgo C. (2016). Why Information Grows. Moscow: Eksmo (in Russian).
Inozemtsev V.L. (2017). The Sovereign Himself. Available at: (accessed: December 2018, in Russian).
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Yoon V.O. (2019). The Content of the Concept of Quality in the Economy. Moscow: Nauka (in Russian).

Volkova M.I. Russian and European population's quality of life analysis with the instruments of common principal components (CPC)
Economics and mathematical methods
, 2019, 55 (3), 34-46.

      Central Economics and Mathematics Institute of RAS, Moscow, Russia; E-mail:
This study was carried with financial support by the Russian Science Foundation (project 17-18-01080).

Abstract. For a number of frequency characteristics of several variables common principal components for period 2011-2015 using the STATIS method is constructed separately for the Russian regions and the European countries. For it, data from RLMS and EUROBAROMETER was used. The selection of criteria for the analysis was carried within the procedure of assessing -criteria for ordinal variables. Estimates of material well-being level, status of respondents, as well as a frequency of alcohol consumption, debt payment difficulties, assessment of immigration and unemployment problem and others are used. Within the framework of STATIS method, it was possible to identify interrelated indicators that form the maximum contribution to the compromise space. The compromise space is built for all the time intervals and features. The methods for calculating the elements of the compromise (generalized) matrix are proposed and tested taking into account the criterion of maximum informativeness. Within the compromise space, groups of the regions (for Russia) and the European countries have been identified. The elements of count matrix obtained as a result of singular decomposition of the compromise matrix are used as criteria of division into groups. The novelty of the research is based on the application of common principal components methodology for subjective data (ordinal variables). The data from the Russian and European surveys are compared.
Keywords: quality of life, life satisfaction, multidimensional statistical analysis, common principal components, RLMS, EUROBAROMETER.
JEL Classification: C10, C19, C39, C80, D10, I30, I31.
DOI: 10.31857/S042473880004678-4

      REFERENCES (with English translation or transliteration)
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Kendall M., Stewart A. (1973). The Advanced Theory of Statistics. Vol. 2: Inference and Relationship. Gal'chuk L.I., Terekhin A.T. (trans.), Kolmogorov A.N. (ed.). Moscow: Nauka, Fizmatlit (in Russian).
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Lavit C., Escoufier Y., Sabatier R., Traissac P. (1994). The ACT (STATIS Method). Computational Statistics & Data Analysis, 18, 97-119.
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Ratnikova T., Furmanov K.K. (2014). Panel Data Analysis and Data on the Duration of States. Textbook. Higher School of Economics. Moscow: Izd. dom Vysshei shkoly ekonomiki (in Russian).
Rivadeneira F.J., Figueiredo A.M.S., Figueiredo F.O.S., Carvajal S.M., Rivadeneira R.A. (2016). Analysis of Well-being in OECD Countries Through STATIS Methodology. HOLOS, 7, 335-351.
Suvorova V.A. (2018). Migration crisis in Europe: problems of forced migration. Power (IS RAS magazine), 1, 176-179 (in Russian).
Vermunt J.K., Magidson J. (2005). Factor Analysis with Categorical Indicators: A Comparison between Traditional and Latent Class Approaches. In: Quantitative methodology series. New Developments in Categorial Data Analysis for the Social and Behavioral Sciences.
Ark L.A. van der, Croon M.A., Sijtsma K. (eds). Mahwah: Lawrence Erlbaum Associates Publishers, 41-62.
Volkova M.I. (2017). Determining of Factors of Life Satisfaction in Russia and European countries. Social Policy and Sociology, 5, 6-15 (in Russian).
Yakubov A.H. (2009). Objectives, Criteria and Methodological Approaches to the Optimization of Rural Settlements in the Municipal District. Herald of Chelyabinsk State Pedagogical University, 26 (164), 104-109.
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Beklaryan G.L. Aggregated simulation model of a region: problems of Krasnoyarsk Region
Economics and mathematical methods
, 2019, 55 (3), 47-61.

      CEMI RAS, Moscow, Russia; E-mail:

Abstract. The article presents an approach to the rational management of the region on the example of the Krasnoyarsk region using the methods of system dynamics. A simulation model of the region is developed, and the possibility of optimizing the key characteristics of such a system through the rational management of multiple parameters, such as the rate of construction of new housing, the rate of growth of the housing services' costs, the rate of construction of social infrastructure (gardens, schools, hospitals), etc. The suggested model allows forming the forecast dynamics of the most important macroeconomic characteristics of the region, taking into account the internal direct and backward linkages between the various elements of such a system and the existing restrictions. The computer implementation of this model is performed in the simulation system Powersim, which supports the methods of system dynamics, as well as the possibility of finding suboptimal solutions using genetic optimization algorithms. An important optimization problem of the region to maximize the integral index - the Gross Regional Product under multiple constraints is formulated. To solve this optimization problem, a genetic optimization algorithm (GA) was chosen, the feature of which is the aggregation of the target functional with a simulation model of the region (implemented in Powersim). Numerical studies have been carried out to predict the GRP of the Krasnoyarsk Region under various scenario conditions, in particular, for the basic scenario, in which the current values of the control parameters of the system are stored and for the best scenario, in which the values of the corresponding control parameters are calculated as a result of solving the problem of the formulated optimization problem using the created optimization module (genetic algorithm). With the help of a simulation model on real data we demonstrated the possibility of improving the economic situation in the Krasnoyarsk Region, mainly due to increased investment in human capital, affecting the dynamics of scientific and technological progress and GRP, respectively.
Keywords: simulation modeling, regional economy, system dynamics, Krasnoyarsk Region.
JEL Classification: B22, 63, R11, R58.
DOI: 10.31857/S042473880005769-4

      REFERENCES (with English translation or transliteration)
Aivazian S.A., Afanasiev M.Y, Kudrov A.V. (2016). Models of Productive Capacity and Technological Efficiency Evaluations of Regions of the Russian Federation Concerning the Output Structure. Economics and Mathematics Methods, 1, 28-44 (in Russian).
Akopov A.S. (2010). On the Issue of Developing of Intelligent Control Systems of Complex Organizational Structures (part I): Mathematical Support for Control System of the Vertically Integrated Oil Company Investment Activities. Problemy upravleniya, 6, 12-18 (in Russian).
Akopov A.S. (2012). System Dynamics Modeling of Banking Group Strategy. Business-Informatics, 2, 10-19 (in Russian).
Akopov A.S. (2011). On the Issue of Developing of Intelligent Control Systems of Complex Organizational Structures (part II): Software Support for Control System of the Vertically Integrated Oil Company Investment Activities. Problemy upravleniya, 1, 47-54 (in Russian).
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Beklaryan L.A.*, Khachatryan N.K.** Dynamic models of cargo flow organization on railway transport
Economics and mathematical methods
, 2019, 55 (3), 62-73.

      * Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia
      **National Research University "Higher School of Economics"
The work was carried with partial financial support by the Russian Foundation for Basic Research (projects 19-01-00147 and 19-010-00958).

Abstract. This article is devoted to mathematical modeling of the process of organization of railway transportation on the transport network, which is a long section of the road with a large number of intermediate stations and located between them railway tracks for temporary storage of cargo. We investigate a model that predicts dynamics of congestion of stations and streams arising in the transportation network, under a given procedure traffic that uses the two technologies, the same for all stations. The first technology is based on the normative rules of interaction of neighboring stations. According to it, the intensity of the reception and dispatch of goods at an arbitrary station should depend on the workload of neighboring stations. The second technology uses the technical capabilities of the stations, and is based on the interaction of the station with neighboring railway tracks. An integral part of the organization of cargo transportation is a control system. This model uses a simple control system, which is that the volume of goods at neighboring stations must coincide with the time lag common to all stations. This model is described by a system of differential equations satisfying nonlocal linear restrictions. For this model the modes of cargo transportation satisfying the given control system are investigated. Such modes are described by solutions of the traveling wave type and two types of their expansions. One type of expansion is associated with the adjustment of transportation technologies and allows discontinuous solutions, the second type of expansion is associated with the weakening of the control system and allows the feasibility of nonlocal linear constraints with a given error. Stationary modes of transportation are investigated for stability.
Keywords: mathematical model, organization of cargo transportation, control system, solutions, quasi-solutions, stationary solutions, stability, numerical realization.
JEL Classification: C63.
DOI: 10.31857/S042473880005780-7

      REFERENCES (with English translation or transliteration)
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Braginsky O.B.*, Tatevosyan G.M.**, Sedova S.V.*** Managing developmental programs (on the example of the chemical industry)
Economics and mathematical methods
, 2019, 55 (3), 74-85.

      Central Economics and Mathematics Institute, Russian Academy of Sciences Moscow, Russia;
This article was prepared with the financial support of the Russian Foundation of Fundamental Research (project 17-06-00198).

Abstract. The article is devoted to the problem of economic mechanism of the governmental programs for industrial and regional development. The information and analytical base of the study consists of two governmental programs for development of the Russian petrochemical complex. The analysis of the development of this complex compared with global trends in the development of petrochemical chemistry. In accordance with the objective of the work, the projects of the investment part of these programs were divided into three groups: high-tech projects and megaprojects for mass production public demand, both corresponding to the global trends in petrochemistry as well as import-substituting projects. The main elements of the economic mechanism of development programs are considered. The focus is on pricing. The necessity of applying contract prices that are not subject to market fluctuations and at the same time ensure a sufficient level of profitability is proved. To stimulate an advanced level of investment in the most promising projects, it is recommended to establish incentive price premiums. A modification of the multi-criteria optimization model, designed to form the structure of the investment part of the development program, is presented. In the model, there is an agreement on the amount of financing and the timing of the launch of projects, on the one hand, and the need for funds of the Federal Budget, reinvested profits and credit, on the other. An approach is proposed that allows using the model to study the effect of prices on products produced within the framework of the program being developed, its structure and indicators. To study the impact of the proposed economic mechanism on the structure of the investment part of the program, experimental calculations were carried out, which showed its significant improvement. However, this impact was limited. The conclusion is made about the need to improve the quality of the original structure of the designed program.
Keywords: economic mechanism, program, investment project, pricing, profitability.
JEL Classification: 37, L52, C61, C88.
DOI: 10.31857/S042473880004710-0

      REFERENCES (with English translation or transliteration)
Akhobadze T.D. (2010). Methods of optimizing investment programs in the real economy. Authorized summary of the Candidate of Science (Economics) thesis. Saint Petersburg: Izdatel'stvo SPbGU (in Russian).
Alfares H.K., Al-Amer A.M.J., Saifuddin S. (2002). A Mathematical Programming Model for Optimum Economic Planning of the Saudi Arabia Petrochemical Industry. In: "The 6th Saudi Engineering Conference". December, 14-16. Dhahran: KFUPM.
Al-Qahtani A. (2008). A Model for the Global Oil Market: Optimal Oil Production Levels for Saudi Arabia. Colorado School of Mines (Doctoral dissertation, Colorado School of Mines).
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Braginskiy O.B., Tatevosyan G.M., Sedova S.V., Magomedov R.Sh. (2017a). Governmental Programs of Industrial and Territorial Development: Methodological and Practical Issues. Preprint WP/2017/325. Moscow: CEMI RAS (in Russian).
Braginskiy O.B., Tatevosyan G.M., Sedova S.V. (2017b). State Development Programs: Ways to Improve. Economics and Mathematical Methods, 53, 4, 3-12 (in Russian).
Braley R., Myers S. (2004). Principles of Corporate Finance. Trans. from English N. Baryshnikova. Moscow: ZAO Olimp-Business (in Russian).
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Il'ichev V.G. Economic and evolutionary aspects of optimum fishing
Economics and mathematical methods
, 2019, 55 (3), 86-99.

      South Scientific Center (SSC) RAS, Rostov-on-Don, Russia E-mail:
The publication is prepared as realization of GZ SSC RAS (project AAAA-A18-118122790121-5) and also of a grant of the Russian Foundation for Basic Research (project 18-01-00453).

Abstract. Within discrete ecology-evolutionary models the problem of collecting long-term fish catch in the two-zone reservoir is investigated. It is shown that taking into account behavioral adaptation of fish population its catch decreases. When the reservoir is divided into two zones (market fishing and the reserve), optimal catch significantly depends on a ratio of ecological capacities of these water areas that is of fodder resources. To solve theoretical and practical problems we used methods of non-linear analysis and dynamic programing, where Bellman function determined maximum catch income. The novelty of our work is a disclosure of unexpected economic and biological effects caused by the adaptation of fish population behavior to the catching processes. If both zones are fishing, then the paradox strategy of catch of one of the competing fishermen connected with temporary reduction of the catch is possible. It will lead to deformation of a fish migration routes with the preference of the first, non-fishing, zone. It is strange that after optimal catch in the area, this area becomes still more attractive to the fish population. The concept of interior prices for fish stocks in some or that area is introduced Interior prices can be used as a tax on unit of the caught fish. In this case the problem of long-term optimization comes down to the solution of a problem of maximizing one-year catch. Spatial heterogeneity of interior prices allows designing various speculative mechanisms of exchange of the consumed resources.
Keywords: long-term fishing, optimization, spatial adaptation, interior prices.
JEL Classification: Q57.
DOI: 10.31857/S042473880005778-4

      REFERENCES (with English translation or transliteration)
Abakumov A.I., Israeli Yu.G. (2017). The Stabilizing Role of Structure of Fish Population in the Conditions of Trade at Accidental Influences of the Habitat. Computer Researches and Modeling, 9, 4, 609-620 (in Russian).
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Economic Transformation and Evolutionary Theory of Y. Shumpert (2004). In the Collection of Articles of the V International Symposium on Evolutionary Economy. Russia. Pushchino, on September 25-27, 2003. Moscow: Institute of Economics of RAS (in Russian)
Il'ichev V.G., Il'icheva O.A. (2018). Spatial Adaptation of Populations in Ecology Models. Biophysics, 63, 2, 373-381 (in Russian).
Il'ichev V.G., Il'icheva V.V. (2014). Spatial Adaptation and Optimum Trade of Fish Populations. Economics and Mathematical Methods, 50, 3, 119-129 (in Russian).
Il'ichev V.G., Rokhlin D.B., Ugolnitsky G.A. (2000). About Economic Mechanisms of Management of Bioresources. Journal of Computer and Systems Sciences International, 4, 104-110 (in Russian).
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Svirezhev Yu.M., Pasekov V.P. (1982). Fundamentals of Mathematical Genetics. Moscow: Nauka (in Russian).

Kotliarov I.D. Economic effect of brand - problems of evaluation
Economics and mathematical methods
, 2019, 55 (3), 100-108.

      National Research University Higher School of Economics, St. Petersburg, Russia; E-mail:

Abstract. The present paper contains an analysis of existing methods of evaluation of a brand economic effect (which is understood as the value generated by the brand for the brand owner). These methods are based on the calculation of brand value on the basis of comparison of cash flows generated by brand with cash flows generated by no-brand product. It is demonstrated that on the brand product market brand efficiency should be measured on the basis of comparison of branded products with an imaginary average brand. It is demonstrated that de facto there are brands that generate no additional income and simply allow their owners to operate on brand-dominated markets. It means that the brand value cannot be used as a measure of brand efficiency for these brands. Contrarily to the traditional brand value, the proposed index of brand efficiency may have positive and negative value. The novelty of the research consists in delimitation of notions of brand value and brand efficiency; introduction of the concept of an average brand; description of the model of calculation of its parameters and methods of calculation of all components of brand efficiency listed above. We also propose to introduce the concept of net modified brand value which can be used to measure the integral brand efficiency from the point of view of brand owner.
Keywords: brand, brand valuation, brand value, economic effect of brand.
JEL Classification: E22.
DOI: 10.31857/S042473880005784-1

      REFERENCES (with English translation or transliteration)
Azgal'dov A.A., Karpova N.N. (2006). Valuation of Intellectual Property and Intangible assets. Moscow: International Academy of Valuation and Consulting (in Russian).
Bagiev G.L., Kozeychuk D.A. (2006). Brand Valuation within the Context of Customers' Loyalty. Brand Management, 3, 146-154 (in Russian).
Damodaran A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. L.: John Wiley and Sons.
Davcik N.S., Vinhas da S.R., Hair J.F. (2015). Towards a Unified Theory of Brand Equity: Conceptualizations, Taxonomy and Avenues for Future Research. Journal of Product and Brand Management, 24 (1), 3-17.
Hirose Y. (2002) Ministry of Economy, Trade and Industry, the Government of Japan. The Report of the Committee on Brand Valuation, 24 June.
Kozyrev A.N. (2015). Economics of Intellectual Property: Measurements, Mythology, Mathematical Models. Journal of the Russian Academy of Sciences, 85 (9), 776 (in Russian).
Kozyrev A.N. (2016). Valuation of Intellectual Property: Functional Approach and Mathematical Methods. Moscow: Izdatel'skie Resheniya. Available at: (accessed: May 2019, in Russian).
Kozyrev A.N., Makarov V.L. (2003). Valuation of Intangible Assets and Intellectual Property. Moscow: Interreklama (in Russian).
Negative or Declining Brand Values: Transfer Pricing Issues. An Idea Worth Considering. (2010). Grant Thornton LLP. Official Website. Available at: (accessed: May 2019).
Nikulina K.G. (2012). Methods of Brand Valuation. Modern Science: Actual Problems of Theory and Practice. Series: Economics and Law, 4, 31-16 (in Russian).
Ritson M. (2010). Negative Brand Equity: A BP Death Sentence. Brand Strategy Insider. Available at: (accessed: May 2019).
Salinas G. (2009). The International Brand Valuation Manual. Sussex: John Wiley & Sons Ltd.
Sawaya W.J., Giauque W.C. (1986). Production and operations management. N.Y.: Harcourt Brace Jovanovich.
Standards of Valuation RICS. (2011). Moscow: Alpina Publisher (in Russian).
Starov S.A., Vilkov V.S. (2002). Classification of Main Approaches Towards Brand Valuation in Russian Companies. Journal of the St. Petersburg University. Series 8: Management, 2, 120-133 (in Russian).
Zhukova N. Yu., Matasov G. M. (2014). How to Estimate the Brand Value: A Modification of Hirose Model. In: "Modernization of Economy and Management: II International Scientific and Practical Conference. 27.02.2014", 143-148 (in Russian).

Aleksandrov Y.B. Determining the accuracy of the company's valuation using a comparative approach in emerging markets
Economics and mathematical methods
, 2019, 55 (3), 109-123.

      TCB Bank, Moscow, Russia; E-mail:

Abstract. The main agenda of this research is to find out the most appropriate multiples and select groups of comparable firms for company's value estimation in the main industries of the following emerging countries: Brazil, Russia, India and China (BRIC). In this research we examine a sample for each country for the period since 2009 to 2013. We test the following seven financial multiples: P/S, P/E, P/BV, EV/EBITDA, EV/EBIT, EV/TA, EV/Sales. Each multiple is tested with each of the following methods of selection group of comparable firms: industry, size, growth potential and combinations: industry-size, industry-growth potential, size-growth potential. The whole market is also used as a method of selecting group of comparable firms just for comparison. As a result, we shall find the most precise multiples and methods of selecting groups of comparable firms. In addition, we consider the accuracy of using combinations of the most precise multiples. In conclusion, we find the best multiples and relevant sets of comparable firms, which demonstrate the most precise estimations of firm values. This research reveals potential of using combination of the most common financial multiples, which let us improve valuation accuracy. This article will be useful for theoretical and practical purposes. This work is unique because firstly, it covers emerging markets and secondly it proves that the combinations of financial multiples in some cases show better results.
Keywords: multiples, firm value, company value, comparative approach, emerging markets, valuation.
JEL Classification: G32.
DOI: 10.31857/S042473880005768-3

      REFERENCES (with English translation or transliteration)
Alford A.W. (1992). The Effect of the Set of Comparable Firms on the Accuracy of the Price-earnings Valuation Method. Journal of Accounting Research, 30, 94-108.
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Clarke R.N. (1989). SICs as Delineators of Economic Markets. Journal of Business, January, 17-31.
Copeland T., Koller T., Murrin J. (1990). Valuation: Measuring and Managing the Value of Companies. New York: Wiley.
Damodaran A. (2008). Investment Valuation: Tools and Techniques for Determining the Value of any Asset. Moscow: Al'pina Biznes Buks (in Russian).
European Valuation Standards 2000 (2003). Russian Society of Appraisers. Available at: (accessed: November 2018, in Russian).
Fishman J., Pratt Sh., Griffit K., Yilson K. (2000). Guide to Business Valuations. Moscow: Kvinto-konsalting (in Russian).
International Valuation Standards 2017 (2018). Russian Society of Appraisers (in Russian).
Kosyr Y. (2003). Valuation and Value Management of Industrial Property Enterprises. Dissertation. Moscow. Russian Academy of Sciences (in Russian).
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Kvint V. (2012). The Global Emerging Market: Strategic Management and Economics. Moscow: Biznes Atlas (in Russian).
Mikerin G., Smolyak S. (2010). Evaluation of the Effectiveness of Investment Projects and Property Valuation: Convergence Opportunities. Moscow: CEMI RAS (in Russian).
Minjina D.I., Brezeanu P., Huidumac C. (2010). Selecting the Group of Comparable Firms for Valuation by Multiples on Bucharest Stock Exchange. Economic Computation and Economic Cybernetics Studies and Research, 44, 183-200.
Rutgeiser V. (2007). Business valuation. Moscow: Maroseika (in Russian).

Smolyak S.A. Influence of deterioration of machinery and equipment on the dynamics of their market value
Economics and mathematical methods
, 2019, 55 (3), 124-140.

      Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; E-mail:
This study was financial partially supported by` the Russian Foundation for Basic Research (project 18-010-99666)

Abstract. Valuing machinery and equipment, it is usually necessary to determine their depreciation/obsolescence. Dependencies of the Percent Good Factor on age are used for this purpose. The shape of such dependencies is not always justified enough. Because of this, the value of fairly old machines is either too low or very high. To eliminate this drawback, this article proposes different descriptions of the process of deterioration for machinery items. At the same time, the deterioration of the operational characteristics of machinery (productivity, failure rate, operating costs, maintenance and repair costs, use-time ratio of the machine) is not tied to age, but to machine's cumulative hours of operation. To calculate the market value of the machine, we use the Discounted Cash Flows method. To avoid subjectivity in the long-term forecasting of cash flows, we apply the principle of anticipated benefits to a small forecast period and combine it with the highest and best use principle. As a result, it takes the following form: the asset value at the valuation date does not exceed the expected value of the discounted cash flow from its use during a small period (including the asset value at the end of the period), and coincides with this expectation if the asset is used in the highest and best way. A mathematical model based on this principle allows us to obtain analytical expressions for the market value of the machine. For each type of machinery and equipment items, the calibration parameters of the model can be selected from the data on the main characteristics and market prices of new and used machinery items of this type. The constructed model was used to estimate depreciation dynamics for two types of construction equipment. The results obtained are in good agreement with the data on the market prices of such equipment of different ages.
Keywords: machinery, equipment, maintenance, repair, market value, depreciation, market approach, anticipation of benefits principle, highest and best use, reliability.
JEL Classification: C61, D24, D46, D81, M41.
DOI: 10.31857/S042473880005785-2

      REFERENCES (with English translation or transliteration)
Asaul A.N., Starinsky V.N., Bezdudnaya A.G., Starovoytov M.K. (2011). Property Valuation: Machinery, Equipment and Vehicles Valuation.
Asaul A.N. (ed.). St. Petersburg: IPEV (in Russian). Assessors' Handbook 581. Equipment and Fixtures Index, Percent Good and Valuation Factors. (2018). California State Board of Equalization. Available at: (accessed: May 2019).
Leyfer L.A. (ed.) (2015). The Handbook of the Machinery and Equipment Appraiser. The adjusting Coefficients and Characteristics of Machinery and Equipment Market. Nizhniy Novgorod: Volga Center for Methodical and Informational Support of Valuation (in Russian).
Leyfer L.A., Kashnikova P.M. (2008). Determination of the Residual Service Life of Machinery and Equipment Based on the Probabilistic Models. Property Relations in the Russian Federation, 1 (86 ), 66-79 (in Russian).
Smolyak S.A. (2008). Problems and Paradoxes of the Machinery and Equipment Valuation. Moscow: RIO MAOC (in Russian).
Smolyak S.A. (2009). Ergo-Dynamic Models of Depreciation of Machinery and Equipment. Economics and Mathematical Methods, 45, 4, 42-60 (in Russian).
Smolyak S.A. (2013). Assessment of Building Depreciation: The Tiemann Model and Its Generalization. Part 1. Property Relations in the Russian Federation, 12 (147), 6-20 (in Russian).
Smolyak S.A. (2014a). Assessment of Building Depreciation: The Tiemann Model and Its Generalization. Part 2. Property Relations in the Russian Federation, 1 (148), 25-35 (in Russian).
Smolyak S.A. (2014b). Overhaul Policy Optimization and Equipment Valuation Concerning Its Reliability. Journal of the New Economic Association, 2 (22), 102-131 (in Russian).
Smolyak S.A. (2014c). Machinery and Equipment Valuation with Regard to their Operation Conditions. Property Relations in the Russian Federation, 8 (155), 70-82 (in Russian).
Smolyak S.A. (2016). Machinery and Equipment Valuation (Secrets of the DCF Method). Moscow: Publishing House Option LLC (in Russian).
Tiemann M. (1970). Reform Proposals for Improving the Income Valuation Approach. Allgemeine Vermessungsnachrichten, 12, 523-530 (in German).
Veyg N.V. (2009). Machinery and Equipment Valuation: Tutorial. St. Petersburg: Publishing house SPSUEF (in Russian).
Yashchura A.I. (2006). The System of Maintenance and Repair of General Industrial Equipment. Moscow: NTS ENAS (in Russian).

Danilov V.I. Skarf's lemma and Brauer's theorem
Economics and mathematical methods
, 2019, 55 (3), 141-146.

      Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia; E-mail:

Abstract. In the paper (Petri, Voorneveld, 2018) it was proposed an elementary proof of Brouwer's fixed point theorem. It was founded on some combinatirial statenet called the no-bullying lemma. In this short note we show that this lemma is a reformulation of the famous Scarf Lemma from classical article (Scarf, 1967). We discuss also a relation of no-bullying to the notion of equilibrated states from paper (Danilov, Sotskov, 1987).
Keywords: KKM-theorem, equilibrated state, no-bullying lemma.
JEL Classification: C44, D81.
DOI: 10.31857/S042473880005771-7

      REFERENCES (with English translation or transliteration)
Vasiliev V.A. (1984). Models of Economacal Exchange and Cooperative Games. Novosibirsk: NGU (in Russian).
Danilov V.I., Sotskov A.I. (1987). Equilibrated States and Theorems on the Core. Optimizatsija, 41, 36-49 (in Russian). [Trans. in: Danilov V.I., Sotskov A.I. (2006). Equilibrated states and theorems on the core. In: "Russian Contributions to Game Theory and Equilibrium theoty" Driessen T., Laan G. van der, Vasil'ev V., Yanovskaya E. (eds). Berlin: Springer, 237-250.]
Danilov V.I. (1998). Lectures on fixed points. Moscow: NES (in Russian).
Danilov V.I. (1999). On Scarf Theorem. Economics and Mathematical Methods, 35, 3, 137-139 (in Russian).
Aubin J.-P. (1984). L'analise non lineare et ses motivations economiques. Paris: Mason.
Aharoni R., Holzman R. (1998). Fractional Kernels in Digraphs. Journal of Comb. Theory, Series B, 73, 1-6.
Ivanov N.V. (2019). Beyond Sperner's Lemma. arXiv:1902.00827[math.AT].
Kuhn H.W. (1968). Simplicial Approximation of Fixed Points. Proceedings of the National Academy of Sciences, 61, 1238-1242.
Petri H., Voorneveld M. (2018). No Bullying! A Playful Proof of Brouwer's Fixed-Point Theorem. Journal of Mathematical Economics, 78, 1-5.
Scarf H. (1967). The Core of N-Person Game. Econometrica, 35, 50-69.


Vol. 55, No. 4

Mindeli L.E., Ostapyuk S.F.*, Fetisov V.P.** On the Results of Long-Term Forecasting of Fundamental and Exploratory Research
Economics and mathematical methods
, 2019, 55 (4), 5-27.

      Institute of Science Development, Russian Academy of Sciences, Moscow, Russia
Work is performed within the framework of the program of fundamental researches of Presidium of the RAS on 2019 year no. 10 "Big challenges and scientific basis for forecasting and strategic planning".
Abstract. In 2018-2019 under the leadership of the Russian Academy of Sciences the procedure of long-term forecasting of fundamental and exploratory researches was implemented. The purpose of this article is to present the results of this prediction for the discussions in the scientific community, the subsequent consideration of the outcome of these discussions in RAS and use of the outcome predictions of fundamental and exploratory research in preparation of further forecasts of the country's scientific and technological development. This article contains a comparison of the results of long-term thematic development forecast for fundamental and exploratory research with the results of the promising areas of scientific and technological development, peer review relevance and world-class projected research on thirteen trends of the science and assessment of their total funding.
Keywords: fundamental and exploratory research, socio-economic development; scientific & technological development, strategic planning, analysis of long-term forecasting.
JEL Classification: E17, B4, I23.
DOI: 10.31857/S042473880006709-8

      REFERENCES (with English translation or transliteration)
Mindeli L., Ostapyuk S., Chernykh S. (2017). Long-Term Forecasting of the Development of Fundamental Science in Russia: Methodological Aspects. The Society and Economy, 10, 5-22.
Mindeli L., Ostapyuk S., Fetisov V. (2018). Global Trends and Challenges That Define the Scientific and Technological Development of Russia. Microeconomics, 5, 7-14.
Mindeli L.E., Ostapyuk S.F., Fetisov V.P. (2019). On Long-Term Prediction of Fundamental and Exploratory Research. Economics and Mathematical Methods, 55, 1, 56-67.

Graborov S.V. Tax Majority Optimization of Citizens' Incomes and Properties
Economics and mathematical methods
, 2019, 55 (4), 28-42

      Central Economics and Mathematics Institute of the Russian Academy of Sciences; E-mail:

Abstract. The article provides one of possible approaches to the non-linear multidimensional optimization of citizens' taxation under the majority rule in case of random number of incomes' and properties' types. The optimality criterion of an initial model is set in a vector form. All the citizens-taxpayers minimize their individual tax payments. The income (revenue) and property taxes are paid under the non-linear scale, and the expenditure (consumption) tax is paid under the linear scale, whereas the tax rates and the thresholds of tax bases are the optimized values. Besides the tax functions and the individual criteria of citizens, ratios of the original model include the aggregate amount limitations of their tax payments, as well as of the admitted values of tax rates. The necessity of including into the model additional conditions for forming coalitions is established. These conditions ensure making a common decision on the optimal tax rates by and for all the participants of the majority group in case of any number of incomes' and properties' types. The conditions, under which the criteria of all the participants of such coalitions become identical, are found. These criteria guarantee making a common decision on the tax rates. The calculation routine of the tax rates on the incomes and properties of the citizens is provided.
Keywords: budget and tax decisions, multi-criteria optimization, majority rule, direct and indirect taxes.
JEL Classification: H2.
DOI: 10.31857/S042473880005773-9

      REFERENCES (with English translation or transliteration)
Arrow K.J. (2004). Social Choice and Individual Values. Moscow: National Research University Higher School of Economics (in Russian).
Atkinson A.B., Stiglitz J.A. (1995). Lectures on the Economic Theory of the Public Sector. Moscow: Aspect Press (in Russian).
Bucovetsky S. (1991). Choosing Tax Rates and Public Expenditure Levels Using Majority Rule. Journal of Public Economics, 46, 1 (October), 113-131.
Calabreze St.M. (2007). Majority Voting over Publicly Provided Goods, Redistribution and Income Taxation. Journal of Public Economic Theory, 9, 2, 319-334.
Caucutt E.M., Imrohoroglu S., Kumar K. (2006). Does the Progressivity of Income Taxes Matter for Human Capital and Grouth? Journal of Public Economic Theory 8, 1, P. 95-118.
Chernik D.G., Shmelev Yu.D. (2011). The Crisis and Taxes. Moscow: Ekonomika (in Russian).
Couglin P.J. (1986). Elections and Income Redistribution. Public Choice, 50, 1-3, 27-91.
Glomm G., Ravikumar B. (1998). Opting out of Publicly Provided Services: A Majority Voting Result. Social Choice and Welfare, 15, 187-199.
Graborov S.V. (2011). Procedures for Calculation of Equilibrium Stable Parameters of Public Choice in Budget and Tax Sphere. Working paper #WP/ 2011/287. Moscow: CEMI RAS (in Russian).
Graborov S.V. (2013). Procedure of Public Choice of the Linear Budgetary and Tax Structure. Economics and Mathematical Methods, 49, 2, 71-86.
Graborov S.V. (2015a). Optimization Models of Budget and Tax Structure: Decision Method and Equivalence of Criterions. Working paper #WP/ 2015/315. Moscow: CEMI RAS (in Russian).
Graborov S.V. (2015b). Majority Optimization of Taxes, Transfers, Prices and Wages. Economics and Mathematical Methods, 51, 1, 80-96.
Graborov S.V., Pitelin A.K. (2016). Macroeconomic Efficiency of Budget and Tax Decisions: Principles and Models. Working paper #WP/ 2016/317. Moscow: CEMI RAS (in Russian).
Graborov S.V., Pitelin A.K. (2017). Majority Optimality of the Direct and Indirect Taxation of the Citizens. Economics and Mathematical Methods, 53, 2, 24-39.
Hariton C., Piaser G. (2007). When Redistribution Leads to Regressive Taxation. Journal of Public Economic Theory 9, 4, 589-606.
Korovkin V.V. (2006). The Fundamentals of the Taxation Theory. Moscow, Economist (in Russian).
Persson T., Tabellini G. (1994). Representative Democracy and Capital Taxation. Journal of Public Economics, 55, 3, 53-70.
Persson T., Tabellini G. (2000). Political Economics: Explaining Economic Policy. London: The MIT Press.
Pushkareva V.M. (2001). The History of Financial Thought and Policies of Taxes. Moscow: Finansy i statistika (in Russian).
Roberts K.W.S. (1977). Voting over Income Tax Schedules. Journal of Public Economics, 8, 3, 329-340.
Roemer J. (1999). The Democratic Political Economy of Progressive Income Taxation. Econometrica, 67, 1, 1-19.
Stiglitz J.E. (1997). Economics of the Public Sector. Moscow: MGU, Infra-M (in Russian).
Tax Reforms. Theory and Practice (2015). Maiburova I.A., Ivanova Yu.B. (eds) Moscow: Yuniti (in Russian).
Yu-Bong L. (2019). Tax Havens, Income Shifting and Redistributive Taxation. Journal of Public Economic Theory, 21, 1, 81-97.
Zakharov A.V. (2009). The Methods of Political Competition: Literature Review. Economics and Mathematical Methods, 45, 1, 110-128.
Zanadvorov V.S., Kolosnitsyna M.G. (2006). The Economic Theory of the Public Finance. Moscow, Higher School of Economics (in Russian).

Galenkova A.D.*, Mariev O.S.**, Nikitin M.V.***, Yunusova I.M.**** Econometric Study of Bubbles in the Russian Real Estate Market
Economics and mathematical methods
, 2019, 55 (4), 43-56.

      Graduate School of Economics and Management, Ural Federal University named after the first President of Russia B.N. Yeltsin, Ekaterinburg, Russia
The research was supported by a grant from the Russian Science Foundation (Project No. 19-18-00262 "Modeling of balanced technological and socio-economic development of Russian regions").

Abstract. The authors test the real estate markets of Russian regions for the presence of bubbles using Pedroni cointegration test. Following the theoretical criteria of Arshanapalli and Nelson, in the absence of bubbles, the housing price index should be integrated with such fundamental factors of the housing market, as the mortgage rate, prices for construction products, economic activity and well-being of the population. The authors adapt this criterion to use not only for the index, but also for the value approach in rouble and dollar equivalents to determine the presence of bubbles in the primary and secondary residential real estate markets of Russian regions. Based on the test results, it was concluded that price indices in the primary and secondary real estate markets do not correctly reflect the real collapse of the Russian real estate markets in 2008 and that the conjuncture of Russian real estate markets does not depend on the exchange rate. The novelty of the author's approach consists in combining and expanding existing methods for detecting bubbles in the regional real estate markets. The main result of the study was firstly obtained and empirically proven conclusion that bubbles appeared in the Russian real estate markets and collapsed regardless of the international economic situation.
Keywords: real estate, real estate markets, Russian regions, real estate market bubbles, modeling, econometric testing, Pedroni test.
JEL Classification: R31, C33, C46.
DOI: 10.31857/S042473880006888-5

      REFERENCES (with English translation or transliteration)
Adams Z., Fuss R. (2010). Macroeconomic Determinants of International Housing Markets. Journal of Housing Economics, 19, 38-50.
Agnello L., Schuknecht L. (2011). Booms and Busts in Housing Markets: Determinants and Implications. Journal of Housing Economics, 20, 171-190.
Aoki K., Proudman J., Vlieghe G. (2014). House Prices, Consumption and Monetary Policy: A Financial Accelerator Approach. Journal of Financial Intermediation, 13, 414-435.
Arshanapalli B., Nelson W. (2008). A Cointegration Test to Verify the Housing Bubble. The International Journal of Business and Finance Research, 2, 2, 35-43.
Beltratti A. (2015). International House Prices and Macroeconomic Fluctuations. Journal of Banking and Finance, 34, 533-545.
Buiter W. (2012). Housing Wealth Isn't Wealth. National Bureau of Economic Research, 14204, 1-23.
Case K.E., Shiller R.T. (2003). Is There a Bubble in the Housing Market? Brookings Papers on Economic Activity, 2, 299-342.
Corbae D., Quintin E. (2013). Leverage and the Foreclosure Crisis. National Bureau of Economic Research, 19323, 1-70.
Dufrenot G. (2015). The Changing Role of House Price Dynamics over the Business Cycle. Economic Modelling, 29, 1960-1967.
Friedman J., Ordway N. (1997) Income property appraisal and analysis. Trans. from English. Moscow: Delo Publ (in Russian).
Giglio S., Maggiori M. (2014). No-Bubble Condition: Model-Free Tests in Housing Markets. NBER Working Paper 20154.
Glaeser E., Gyourko J. (2008). Housing Supply and Housing Bubbles. National Bureau of Economic Research. No. 14193, 1-60.
Grigorev L., Ivashchenko A. (2010). The Theory of Cycle under the Crisis Blow. Issues of Economics, 10, 31-55 (in Russian).
Iacoviello M. (2012). House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle. The American Economic Review, 95, 339-764.
Im K., Pesaran M., Shin Y. (2003). Testing for Unit Roots in Heterogeneous Panels. Journal of Econometrics, 115, 53-74.
Maksimov S.N., Bachurinskaya I.A. (2009). Managing External Effects on the Real Estate Market. Problems of Modern Economics, 3 (31), 379-381 (in Russian).
Mikhed V., Zemcik P. (2009). Testing for Bubbles in Housing Market: A Panel Data Approach. Journal of Real Estate Financial Economics, 38, 366-386.
Pedroni P. (1999). Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors. Oxford Bulletin of Economics and Statistics. Special Issue, 653-670.
Rodionova N.V. (2009). Specificity of Pricing on the Market of Habitation and the Factors Influencing the Prices of the Real Estate. Audit and Financial Analysis, 2, 406-411 (in Russian).
Sternik G.M., Sternik S.G. (2009). Analysis of Real Estate Market for Professionals. Moscow: Ekonomika (in Russian).
Wagner M., Hlouskova J. (2007). The Performance of Panel Cointegration Methods: Results from a Large Scale Simulation Study. Economic series: Institute for Advanced Studies, Vienna.

Abramyan S.I.i,*, Ryumina Ye.V.ii,**, Fedotov A.A.ii,*** Assessment of the Global Purposes' Impact of Sustainable Development on Human Potential
Economics and mathematical methods
, 2019, 55 (4), 57-67.

      iMIREA - Russian Technological University, Moscow, Russia
      iiInstitute for Socio-Economic Studies of Population, Russian Academy of Sciences, Moscow, Russia

Abstract. The purpose of this research is to assess the level of human potential in the Russia's regions and to determine whether it contributes to the achievement of the "Goals of sustainable development for the period until 2030". These "Global Goals" were proposed by the United Nations Development Program, adopted internationally by most countries, including Russia, and officially became effective on January 1, 2016. The article analyzes how the attitude of society to human development is changing in the course of history and how it is interpreted by the modern concept of sustainable development in the United Nations Development Program. Six indicators characterizing various aspects of human potential are offered. Interregional analysis of the selected components of human potential is carried out and the most prosperous and unfavorable regions in this regard are identified. The results of the analysis can be used to choose priority areas in the development of individual regions. Since Russia has not yet developed national indicators for the achievement of the "Global Sustainable Development Goals", the study formed such indicators based on official statistics of the Russia's regions. As a result, 16 indicators were proposed for 8 Goals, and their correlation analysis with human potential indicators is carried out. For this purpose, statistical data is collected, processed and analyzed for the period of 9 years in 85 regions of Russia. The results of our research can be used to formulate a strategy for achieving the "Sustainable Development Goals" for individual regions, as well as for developing the priority trends in the regions.
Keywords: human development, sustainable development, human potential, quality of population, statistical analysis, interregional analysis.
JEL Classification: Q01.
DOI: 10.31857/S042473880006773-9

      REFERENCES (with English translation or transliteration)
Bobylyov S.N., Grigoriev L.M. (2016). The Report on Human Development in the Russian Federation for 2016. Moscow: Russian Government Analytical Centre (in Russian).
Daly H. (1968). On Economics as a Life Science. The Journal of Political Economy, 76, 3, 392-406.
Diverse World (2014). New York: UNDP.
Forrester J.W. (1971). World Dynamics. Cambridge. Wright-Allen Press, Inc.
Frolov I.T. (1999). Human Potential: Experience of an Integrated Approach. Moscow: Editorial URSS (in Russian).
Human Development Report (1990). N.Y.: Oxford University Press.
Human Development Report (2014). The Rise of the South: Human Progress in a Human Development Report 2014: Sustaining Human Progress: Reducing Vulnerabilities and Building Resilience. New York: UNDP.
Ivanov S.A. (2012). Formation of Innovative Competences and Properties of Human Potential: The report. The XIII April International scientific conference "Modernization of Economy and Society" (on April 3-5, 2012, Moscow). Available at: (accessed: 05.02.2018, in Russian).
Kravchenko E.N., Sharkevich I.V. (2011). Particularly Human Development Regions in Modern Russia. Economy of Region, 3, 71-79 (in Russian).
Lokosov V.V., Ryumina E.V., Ulyanov V.V. (2015). Regional Differentiation of Human Potential Indicators. Economy of Region, 4, 185-196 (in Russian).
Meadows D.H., Randers J., Meadows D.L., Behrens W.W. (1972). The Limits to Growth: A Report for the Club of Rome's Project on the Predicament of Mankind. New York: Universe Books.
Models of Doom (1973). A Critique of the Limits to Growth. New York: Universe Books.
Rimashevskaya N.M., Migranova L.A., Toksanbaeva M.S. Human and Labour Potential of the Russian Regions. Population, 3, 106-119 (in Russian).
Ryumina E.V. (2014). Ecological Characteristic of Quality of the Population. Economy of Region, 3, 82-90 (in Russian).
Ryumina E.V. (2017). Characteristic of Ecological Aspects of Quality of Life and their Reflection in the Index of Human Development. "Strategic Planning and Development of the Enterprises. Section 4: Materials of the Eighteenth All-Russian Symposium". Kleyner G.B. (ed.). Moscow: CEMI RAS, 811-814 (in Russian).
Simovici D.A., Chabane D. (2014). Mathematical Tools for Data Mining. Second edition. London: Springer-Verlag.
Transforming our World: The 2030 Agenda for Sustainable Development (2015). United Nations.
Weizsaecker E. von, Wijkman A. (2018). Come On! Capitalism, Short-termism, Population and the Destruction of the Planet. New York: Springer.

Grebennikov V.G.*, Magomedov R.Sh.** Budgetary Self-Sufficiency as a Problem of the Governmental Programming of Regional Development
Economics and mathematical methods
, 2019, 55 (4), 68-77.

      Central Economics and Mathematics Institute, Russian Academy of Sciences

Abstract. An approach to the structural analysis of the governmental program of macro-region development which allows controlling the levels of regional budgetary self-sufficiency is proposed. This approach is applied to the "Development of the North Caucasian Federal District until 2025" Governmental Program of the Russian Federation. Two interrelated hypotheses about the presence of negative feedback between the share of program activities of a market nature in the expenditures of the regional consolidated budget and the share of non-repayable transfers in its revenues as well as positive feedback between the share of program activities of a market nature in the expenditures of the regional consolidated budget and the share of taxes on business in its revenues are substantiated. An approach to estimate the validity of the volumes of federal transfers allocated to regions is proposed. For this purpose, an indicator of regional budgetary self-sufficiency potential is introduced. The information and analytical database of the research includes data on the execution of the regional consolidated budgets in 2001-2017 from the Russian Federal Treasury, as well as budget classification of the Russian Ministry of Finance. Conclusions and results of the study can be used in strategic, including budget, planning in order to improve legal support for the management of the governmental programs of regional development.
Keywords: regional development, North Caucasian Federal District, governmental program, program structure, program activities, regional consolidated budget, budgetary self-sufficiency, non-repayable receipts, federal intergovernmental transfers, business taxes, subsidies, budget investments, correlation analysis.
JEL Classification: H53, R58.
DOI: 10.31857/S042473880006774-0

      REFERENCES (with English translation or transliteration)
Belen'kiy V.Z., Grebennikov V.G. (2013). Some Formulations of Ranking and Their Solution Based on the Principle of Consistency. Economics of Contemporary Russia, 3, 59-69 (in Russian).
Braginsky O.B., Tatevosyan G.M., Sedova S.V., Magomedov R.Sh. (2017). Governmental Programs of Industrial and Territorial Development: Methodological and Practical Issues. Working paper # WP / 2017/325. Moscow: CEMI RAS (in Russian).
DonVito P.A. (1969). The Essentials of a Planning-Programming-Budgeting System. Available at: (accessed: 23.10.2015).
Gagarina G.Y., Dzyuba E.I., Gubarev R.V., Fayzullin F.S. (2017). Forecasting of Socio-Economic Development of the Russian Regions. Economy of Region, 13 (4), 1080-1094 (in Russian). doi 10.17059/2017-4-9.
Grebennikov V.G., Magomedov R.Sh. (2018). Balance of Budget Expenditures as a Source for Increasing Regional Budgetary Self-sufficiency. In: "Management of Large-Scale System Development" (MLSD'2018): Proceedings of the Eleventh International Conference (1-3 oct. 2018, Moscow). Vasilyev S.N., Tsvirkun A.D. (eds). Vol. 3: Sections 12-16. Moscow: Institute of Control Sciences by. V.A. Trapeznikova of the Russian Academy of Sciences, 426-432 (in Russian).
Idrisova V., Freinkman L. (2010). The Impact of Federal Transfers over Regional Authorities Behavior. Moscow: Gaidar Institute for Economic Policy (in Russian).
Premchand A. (1989). Government Budgeting and Expenditure Controls: Theory and Practice. Third Printing. Washington: International Monetary Fund.
Solem J., Werner H.D. (1968). PPBS: A Management Innovation. Available at: (accessed: 16.04.2017).
Tatevosyan G.M., Pisareva O.M., Sedova S.V., Simonova N.I. (2004). A Comparative Analysis of the Regional Economic Performance in Russia. Economics and Mathematical Methods, 40 (4), 59-73 (In Russian).
Tatevosyan G.M., Pisareva O.M., Sedova S.V., Toreyev V.B. (2009). Methods for Justifying Investment Programs (Industrial Sector). Preprint # WP/2009/260. Moscow: CEMI RAS (in Russian).
Yermakov V.V. (2017). Measuring the Impact of Interbudgetary Transfers on the Regional Socio-Economic Development. Economics and Mathematical Methods, 53 (3), 18-37 (in Russian).

Volodina E..i,*, V.N. Livshitsii,** On Flood Algorithm for Approximate Solution of Smooth Nonlinear Programming Problems with Linear Constraints of Large Dimension
Economics and mathematical methods
, 2019, 55 (4), 78-88

      iMoscow Technical University of Communications and Informatics, Moscow, Russia
      iiFederal Research Center "Informatics and Management" of the Russian Academy of Sciences, Moscow, Russia

Abstract. The article analyzes researches in the field of formulation of linear and nonlinear transport problems and algorithms for their solution. The scientific works on the optimization of flows in networks are considered, which made a significant contribution to the creation and development of a new economic and mathematical area as a whole and in many respects stimulated the formation of optimization models and their practical use in a number of industries, first of all in the transport. Particular attention is paid to solving the nonlinear programming problem, when the costs at each transport link depend substantially and nonlinearly not only on the link parameters, but also on the total volume and structure of the cargo flow passing through it. That is, the solution of a large-sized nonlinear inhomogeneous transport problem of a network structure is given when setting the initial information about transportation in the form of a large-sized correspondence matrix. An effective method for optimizing the distribution of inhomogeneous flows over a fixed nonlinear transport network is described. Based on the tools of functional analysis, the theorem of the validity of using the conditions of potentiality of the optimal plan for traffic flows in the nonlinear case is proved. The proposed two-stage algorithm for optimizing the step-by-step distribution of inhomogeneous flows over a fixed nonlinear transport network is discussed, based on the given evidence of the legitimacy of the principle of potentiality of an optimal transportation plan being extended to this case.
Keywords: optimal planning, nonlinear programming, linear constraint, transport problem, correspondence matrix, costs, cargo flow, step-by-step flow distribution, two-stage optimization algorithm.
JEL Classification: C5.
DOI: 10.31857/S042473880006776-2

      REFERENCES (with English translation or transliteration)
Belousova N.I., Bushanskij S.P., Vasil'eva E.M., Livchits V.N., Pozamantir E.I. (2004). Improving the Theoretical Foundations Models and Methods for Optimizing the Development of the Road Network. Computer Audit, 3, 114-204 (in Russian).
Belousova N.I., Bushanskij S.P., Vasil'eva E.M., Livchits V.N., Pozamantir E.I. (2008). Information Technology of Synthesis of Complex Network Structures of Non-Stationary Russian Economy: Models, Algorithms, Software Implementation. Audit and Financial Analysis, 1, 50-88 (in Russian).
Bertalanffy L. von (1950). An Outline of General Systems Theory. British Journal for Philosophy of Science, 2, 1, 139-164.
Dubovickij A.YA., Milyutin A.A. (1965). Tasks for Extremum in the Presence of Restrictions. Computational Mathematics and Mathematical Physics, 3, 395-453 (in Russian).
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Labsker L.G. The Property of Synthesizing by the Wald-Savage Criterion and Economic Application
Economics and mathematical methods
, 2019, 55 (4), 89-103.

      Financial University under the Government of the Russian Federation, Moscow, Russia; E-mail:
The author thanks the Corresponding member of the Russian Academy of Sciences, Doctor of Economics, Professor G.B. Kleiner for the opportunity to make a presentation at his scientific seminar at the Financial University under the Government of the Russian Federation, for discussing the results and constructive comments that contribute to a deeper analysis of the problems considered in the article.

Abstract. In the game with nature, the synthetic Wald-Savage criterion is defined as the principle of optimality, which makes possible to evaluate the optimality of strategies from a synthetic (joint) point of view of wins and risks. The definition of the synthesized strategy is given, i.e. a strategy that is optimal by the Wald-Savage criterion and is not optimal by either the Wald criterion or the Savage criterion. Introduced into the property of synthesizing, which consists in the existence of a synthesized strategy. Scientific novelty consists in solving the formulated problem of synthesizing, which consists in finding the necessary and sufficient conditions for the Wald-Savage criterion to have no synthesizing properties. Sufficient conditions are also of practical importance in analyzing the problems of making optimal economic decisions, since the fulfillment of these conditions means that it does not make sense to use the Wald-Savage criterion to find synthesized strategies. Moreover, the verification of sufficient conditions does not require reference to the Wald-Savage criterion itself, but is based only on the component criteria. However, the exploitation of the Wald-Savage criterion in the absence of its synthesis properties is not absolutely useless, since it reveals the dependence of the application of the Wald and Savage criteria on the determined payoff indicator. The application of the obtained results is illustrated on the solution of the problem of economic content on the optimal choice of the technological mode of production.
Keywords: playing with nature, Wald criterion, Savage criterion, payoff-indicator, Wald-Savage criterion, synthesized strategy, Wald-Savage synthesizing problem, synthesizing problem solving, two-criterion optimization problem, technological methods of production, need in products, optimal choice of production method.
JEL Classification: D81.
DOI: 10.31857/S042473880006775-1

      REFERENCES (with English translation or transliteration)
Labsker L.G., Yashchenko N.A., Amelina A.V. (2011a). Optimizing the Choice of a Corporate Bank Borrower Based on the Synthetic Wald-Savage Criterion. Financial Analytics: Problems and Solutions, 34 (76), 43-54 (in Russian).
Labsker L.G., Yashchenko N.A., Amelina A.V. (2011b). Formation of the Priority of Bank Lending to Corporate Borrowers According to the Synthetic Wald-Savage Criterion. Finance and Credit, 38 (518), 31-41 (in Russian).
Labsker L.G., Yashchenko N.A., Amelina A.V. (2012). The Priority of Bank Lending to Corporate Borrowers: The Formation of a Priority Order Based on the Synthetic Wald-Savage Criterion. Saarbrucken: LAMBERT Academic Publishing GmbH & Co. KG (in Russian).
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Labsker L.G. (2014). The Theory of Optimality Criteria and Economic Decisions. Moscow: KNORUS (in Russian).
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N.M. Svetlov Non-Parametric Production Frontier in a Computable Partial Equilibrium Model
Economics and mathematical methods
, 2019, 55 (4), 104-116.

      Central Economics and Mathematics Institute RAS, Moscow, Russia; E-mail:

Abstract. A computable mathematical model of partial equilibrium is developed, which supply functions are derived at the run-time from the data that define suppliers' production frontiers in a non-parametric form. Unlike the common computable partial equilibrium models, the proposed model avoids sophisticated estimations of supply function parameters, achieves better credibility of the model outcome. Such a model allows a researcher to study the response of markets to the varying amount of resources as well as in the production technologies and climate conditions, avoiding assumptions (which are difficult to test) on how such factors affect the supply functions. For the purpose of ensuring acceptable computational properties of the model, the non-parametric production frontier is represented by simultaneous inequations derived from the duality theory, instead of the common representation as a linear program. Furthermore, the paper presents the application of the developed model to the analysis of price change in the cattle and poultry, milk and grain markets in Federal subjects of the Russian Federation (within 2013) in the scenario that partially activates the current reserves for improving territorial and industrial structure of the Russian agriculture. The model specification considers transport links between the Federal subjects, natural agricultural zones and uncertainty.
Keywords: computable model, partial equilibrium, policy analysis, duality theory, non-parametric production frontier, markets of agricultural products.
JEL Classification: C63; Q11; Q18.
DOI: 10.31857/S042473880006779-5

      REFERENCES (with English translation or transliteration)
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Churin Yu.G. Minimization Method for Solution of Transport and Economic Problem
Economics and mathematical methods
, 2019, 55 (4), 117-122.

      "Higher Mathematics" of FSEI HE Kostroma SA, Kostroma, Russia; E-mail:

Abstract. The method of minimization of function which represents the sum of modules of the binomial being the differences of an independent variable and a set of these numbers is considered. Such function determines the sum of the distances measured by length of an arch of some set line from the points belonging to this line to some point (on the same line). Need of minimization of this function can arise for solution of the following question. On the thoroughfare (the railroad, the highway, the river, etc.) there are operating manufacturing enterprises, and it is necessary to deliver their products for further processing to the enterprise which is planned to be located on this highway. It is required to define location of this enterprise proceeding from a condition of the smallest transportation costs.
Keywords: number module, function minimization, function derivative.
JEL Classification: C61.
DOI: 10.31857/S042473880006777-3